Surface Area and Volume of a Right Circular Cylinder- 1 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

 Page 1


Q u e s t i o n : 1
Curved surface area of a right circular cylinder is 4.4 m
2
. If the radius of the base of the cylinder is 0.7 m, find its height.
S o l u t i o n :
In the problem it is given that the Curved Surface Area of the cylinder is .
We know that,
Curved Surface Area of a cylinder 
Where,  radius of the cylinder and  height of the cylinder
In the given problem,  and h is to be found out.
Let us substitute all the given values in the formula for Curved Surface Area of the cylinder.
We have,
For simplifying the, this can be written as,
Now, clearly m
Therefore, the height of the cylinder is 1 meter.
Q u e s t i o n : 2
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
S o l u t i o n :
The following data is given in the problem:
h = 28 m
Diameter = 5 cm
We are asked to find the Total radiating surface, which is nothing but the Total Surface Area of the cylinder.
The height of the cylinder is in meters, so let us first convert it into centimeters.
h = 2800 cm
Also, the diameter of the cylinder is given, but we want the radius.
The formula for finding out the Total Surface Area is:
Total Surface Area
Substituting the above values in this equation, we have
Total Surface Area
Total Surface Area 
Total Surface Area 
Therefore, the answer to this problem is 
Q u e s t i o n : 3
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m
2
.
S o l u t i o n :
The data given in the problem is as follows:
Diameter of the cylinder =50cm
Height = 3.5m
Painting charges = Rs.12.50 per m
2
We have to find the total cost of painting the pillar
To find the cost of painting the pillar, we should first find the Curved Surface Area of the pillar using the given data.
Curved Surface Area 
r = 
Since the painting charges are given in terms of , we shall convert the radius from centimeters to meters.
r = 0.25m
Substituting the values in the formula for Curved Surface Area, we have
Curved Surface Area
Curved Surface Area = 5.5 m
2
It is given that, for 1 m
2 
the cost of painting is Rs.12.50
Therefore,
Total cost of painting the pillar = 
Page 2


Q u e s t i o n : 1
Curved surface area of a right circular cylinder is 4.4 m
2
. If the radius of the base of the cylinder is 0.7 m, find its height.
S o l u t i o n :
In the problem it is given that the Curved Surface Area of the cylinder is .
We know that,
Curved Surface Area of a cylinder 
Where,  radius of the cylinder and  height of the cylinder
In the given problem,  and h is to be found out.
Let us substitute all the given values in the formula for Curved Surface Area of the cylinder.
We have,
For simplifying the, this can be written as,
Now, clearly m
Therefore, the height of the cylinder is 1 meter.
Q u e s t i o n : 2
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
S o l u t i o n :
The following data is given in the problem:
h = 28 m
Diameter = 5 cm
We are asked to find the Total radiating surface, which is nothing but the Total Surface Area of the cylinder.
The height of the cylinder is in meters, so let us first convert it into centimeters.
h = 2800 cm
Also, the diameter of the cylinder is given, but we want the radius.
The formula for finding out the Total Surface Area is:
Total Surface Area
Substituting the above values in this equation, we have
Total Surface Area
Total Surface Area 
Total Surface Area 
Therefore, the answer to this problem is 
Q u e s t i o n : 3
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m
2
.
S o l u t i o n :
The data given in the problem is as follows:
Diameter of the cylinder =50cm
Height = 3.5m
Painting charges = Rs.12.50 per m
2
We have to find the total cost of painting the pillar
To find the cost of painting the pillar, we should first find the Curved Surface Area of the pillar using the given data.
Curved Surface Area 
r = 
Since the painting charges are given in terms of , we shall convert the radius from centimeters to meters.
r = 0.25m
Substituting the values in the formula for Curved Surface Area, we have
Curved Surface Area
Curved Surface Area = 5.5 m
2
It is given that, for 1 m
2 
the cost of painting is Rs.12.50
Therefore,
Total cost of painting the pillar = 
= 68.75
Therefore, the answer to this questions is, Rs.68.75
Q u e s t i o n : 4
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a  metal sheet. How many square metres of the sheet are required for the same?
S o l u t i o n :
The data given in the problem is as follows:
h = 1 m
Diameter = 140 cm
We are asked to find the area of the sheet in square meters required to make this cylinder.
Since it is a closed cylinder, the area of the sheet required to make this will be equal to the Total surface area of the cylinder.
Total surface area 
= =70cm
Since area is asked in square meters, let us convert the radius from centimeters to meters.
r = 0.7m
Substituting the values in the formula for the Total Surface Area of a cylinder, we have
Total Surface Area
Total Surface Area = 7.48
Therefore, the area of sheet required to make this cylinder is 7.48 square meters.
Q u e s t i o n : 5
The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.
S o l u t i o n :
Data given is the problem is as follows:
The cylinder is a hollow cylinder and is open on both sides
Total surface area of the cylinder is 4620 square centimeters
Area of the base ring = 115.5 square centimeters
Height = 7 cm
We are supposed to find the thickness of this cylinder.
We know that,
Total surface area of a hollow cylinder 
Where, r is the inner radius and R is the outer radius of the cylinder.
Now we have,
= 4620
Also, h = 7cm
= 4620
Also, it is given that
Area of base ring = 115.5
That is, = 115.5 …..
1
Substituting for in the above equation, we have
2
115.5 = 4620
=4389
Also, h = 7
Therefore,
.….
2
Now let us again take up equation
1
= 115.5
From equation
Page 3


Q u e s t i o n : 1
Curved surface area of a right circular cylinder is 4.4 m
2
. If the radius of the base of the cylinder is 0.7 m, find its height.
S o l u t i o n :
In the problem it is given that the Curved Surface Area of the cylinder is .
We know that,
Curved Surface Area of a cylinder 
Where,  radius of the cylinder and  height of the cylinder
In the given problem,  and h is to be found out.
Let us substitute all the given values in the formula for Curved Surface Area of the cylinder.
We have,
For simplifying the, this can be written as,
Now, clearly m
Therefore, the height of the cylinder is 1 meter.
Q u e s t i o n : 2
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
S o l u t i o n :
The following data is given in the problem:
h = 28 m
Diameter = 5 cm
We are asked to find the Total radiating surface, which is nothing but the Total Surface Area of the cylinder.
The height of the cylinder is in meters, so let us first convert it into centimeters.
h = 2800 cm
Also, the diameter of the cylinder is given, but we want the radius.
The formula for finding out the Total Surface Area is:
Total Surface Area
Substituting the above values in this equation, we have
Total Surface Area
Total Surface Area 
Total Surface Area 
Therefore, the answer to this problem is 
Q u e s t i o n : 3
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m
2
.
S o l u t i o n :
The data given in the problem is as follows:
Diameter of the cylinder =50cm
Height = 3.5m
Painting charges = Rs.12.50 per m
2
We have to find the total cost of painting the pillar
To find the cost of painting the pillar, we should first find the Curved Surface Area of the pillar using the given data.
Curved Surface Area 
r = 
Since the painting charges are given in terms of , we shall convert the radius from centimeters to meters.
r = 0.25m
Substituting the values in the formula for Curved Surface Area, we have
Curved Surface Area
Curved Surface Area = 5.5 m
2
It is given that, for 1 m
2 
the cost of painting is Rs.12.50
Therefore,
Total cost of painting the pillar = 
= 68.75
Therefore, the answer to this questions is, Rs.68.75
Q u e s t i o n : 4
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a  metal sheet. How many square metres of the sheet are required for the same?
S o l u t i o n :
The data given in the problem is as follows:
h = 1 m
Diameter = 140 cm
We are asked to find the area of the sheet in square meters required to make this cylinder.
Since it is a closed cylinder, the area of the sheet required to make this will be equal to the Total surface area of the cylinder.
Total surface area 
= =70cm
Since area is asked in square meters, let us convert the radius from centimeters to meters.
r = 0.7m
Substituting the values in the formula for the Total Surface Area of a cylinder, we have
Total Surface Area
Total Surface Area = 7.48
Therefore, the area of sheet required to make this cylinder is 7.48 square meters.
Q u e s t i o n : 5
The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.
S o l u t i o n :
Data given is the problem is as follows:
The cylinder is a hollow cylinder and is open on both sides
Total surface area of the cylinder is 4620 square centimeters
Area of the base ring = 115.5 square centimeters
Height = 7 cm
We are supposed to find the thickness of this cylinder.
We know that,
Total surface area of a hollow cylinder 
Where, r is the inner radius and R is the outer radius of the cylinder.
Now we have,
= 4620
Also, h = 7cm
= 4620
Also, it is given that
Area of base ring = 115.5
That is, = 115.5 …..
1
Substituting for in the above equation, we have
2
115.5 = 4620
=4389
Also, h = 7
Therefore,
.….
2
Now let us again take up equation
1
= 115.5
From equation
2 we have . Substitute this in the above equation.
(R – r) is nothing but the thickness of the cylinder.
Therefore, the thickness of the cylinder is cm
Q u e s t i o n : 6
Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.
S o l u t i o n :
Data given in the problem is as follows:
h =7.5 cm
r = 3.5 cm
We are supposed to find the ratio between the Total Surface Area and the Curved Surface Area.
We know that,
Total Surface Area
TSA = 
Curved Surface Area
CSA = 
Therefore,
= 
=
Substituting the values of h and r in the above expression, we have
= 
= = =
Hence the ratio between Total Surface area and Curved Surface Area is 22 : 15.
Q u e s t i o n : 7
A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 3.50 per
1000 cm
2
.
S o l u t i o n :
It is given that,
r = 70 cm
h = 1.4 m
Tin coating rate =  cm
2
We have to find the total cost of coating the cylinder with tin.
Let us first convert h from meters to centimeters.
h = 1.4 m
= 140 cm
Since the cylindrical vessel without lid has to be coated both on the inner side as well the outer side,
Area to be coated = 
=
= 154000 cm
2
Now let us find the total cost of coating this area.
For 1000 cm
2
 the cost of coating is Rs.3.50
For 154000 cm
2 
the cost of coating is given by =539
Therefore the total cost of coating the vessel on both inner and outer sides is Rs.539
Q u e s t i o n : 8
The inner diameter of a circular well is 3.5 m. It is 10 m deep Find:
i
inner curved surface area.
ii
the cost of plastering this curved surface at the rate of Rs 40 per m
2
.
Page 4


Q u e s t i o n : 1
Curved surface area of a right circular cylinder is 4.4 m
2
. If the radius of the base of the cylinder is 0.7 m, find its height.
S o l u t i o n :
In the problem it is given that the Curved Surface Area of the cylinder is .
We know that,
Curved Surface Area of a cylinder 
Where,  radius of the cylinder and  height of the cylinder
In the given problem,  and h is to be found out.
Let us substitute all the given values in the formula for Curved Surface Area of the cylinder.
We have,
For simplifying the, this can be written as,
Now, clearly m
Therefore, the height of the cylinder is 1 meter.
Q u e s t i o n : 2
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
S o l u t i o n :
The following data is given in the problem:
h = 28 m
Diameter = 5 cm
We are asked to find the Total radiating surface, which is nothing but the Total Surface Area of the cylinder.
The height of the cylinder is in meters, so let us first convert it into centimeters.
h = 2800 cm
Also, the diameter of the cylinder is given, but we want the radius.
The formula for finding out the Total Surface Area is:
Total Surface Area
Substituting the above values in this equation, we have
Total Surface Area
Total Surface Area 
Total Surface Area 
Therefore, the answer to this problem is 
Q u e s t i o n : 3
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m
2
.
S o l u t i o n :
The data given in the problem is as follows:
Diameter of the cylinder =50cm
Height = 3.5m
Painting charges = Rs.12.50 per m
2
We have to find the total cost of painting the pillar
To find the cost of painting the pillar, we should first find the Curved Surface Area of the pillar using the given data.
Curved Surface Area 
r = 
Since the painting charges are given in terms of , we shall convert the radius from centimeters to meters.
r = 0.25m
Substituting the values in the formula for Curved Surface Area, we have
Curved Surface Area
Curved Surface Area = 5.5 m
2
It is given that, for 1 m
2 
the cost of painting is Rs.12.50
Therefore,
Total cost of painting the pillar = 
= 68.75
Therefore, the answer to this questions is, Rs.68.75
Q u e s t i o n : 4
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a  metal sheet. How many square metres of the sheet are required for the same?
S o l u t i o n :
The data given in the problem is as follows:
h = 1 m
Diameter = 140 cm
We are asked to find the area of the sheet in square meters required to make this cylinder.
Since it is a closed cylinder, the area of the sheet required to make this will be equal to the Total surface area of the cylinder.
Total surface area 
= =70cm
Since area is asked in square meters, let us convert the radius from centimeters to meters.
r = 0.7m
Substituting the values in the formula for the Total Surface Area of a cylinder, we have
Total Surface Area
Total Surface Area = 7.48
Therefore, the area of sheet required to make this cylinder is 7.48 square meters.
Q u e s t i o n : 5
The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.
S o l u t i o n :
Data given is the problem is as follows:
The cylinder is a hollow cylinder and is open on both sides
Total surface area of the cylinder is 4620 square centimeters
Area of the base ring = 115.5 square centimeters
Height = 7 cm
We are supposed to find the thickness of this cylinder.
We know that,
Total surface area of a hollow cylinder 
Where, r is the inner radius and R is the outer radius of the cylinder.
Now we have,
= 4620
Also, h = 7cm
= 4620
Also, it is given that
Area of base ring = 115.5
That is, = 115.5 …..
1
Substituting for in the above equation, we have
2
115.5 = 4620
=4389
Also, h = 7
Therefore,
.….
2
Now let us again take up equation
1
= 115.5
From equation
2 we have . Substitute this in the above equation.
(R – r) is nothing but the thickness of the cylinder.
Therefore, the thickness of the cylinder is cm
Q u e s t i o n : 6
Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.
S o l u t i o n :
Data given in the problem is as follows:
h =7.5 cm
r = 3.5 cm
We are supposed to find the ratio between the Total Surface Area and the Curved Surface Area.
We know that,
Total Surface Area
TSA = 
Curved Surface Area
CSA = 
Therefore,
= 
=
Substituting the values of h and r in the above expression, we have
= 
= = =
Hence the ratio between Total Surface area and Curved Surface Area is 22 : 15.
Q u e s t i o n : 7
A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 3.50 per
1000 cm
2
.
S o l u t i o n :
It is given that,
r = 70 cm
h = 1.4 m
Tin coating rate =  cm
2
We have to find the total cost of coating the cylinder with tin.
Let us first convert h from meters to centimeters.
h = 1.4 m
= 140 cm
Since the cylindrical vessel without lid has to be coated both on the inner side as well the outer side,
Area to be coated = 
=
= 154000 cm
2
Now let us find the total cost of coating this area.
For 1000 cm
2
 the cost of coating is Rs.3.50
For 154000 cm
2 
the cost of coating is given by =539
Therefore the total cost of coating the vessel on both inner and outer sides is Rs.539
Q u e s t i o n : 8
The inner diameter of a circular well is 3.5 m. It is 10 m deep Find:
i
inner curved surface area.
ii
the cost of plastering this curved surface at the rate of Rs 40 per m
2
.
S o l u t i o n :
Given data is as follows:
Inner diameter of the well = 3.5 m
h = 10 m
Rate of plastering = Rs.40 per square meter
We have to find two things,
1. Inner curved surface area
2. Total cost of plastering the inner curved surface
i
Inner curved surface area = 110
ii Now, let us find the total cost of plastering this area.
It is given that for 1 the cost of plastering is Rs.40
Therefore, for 110 the cost of plastering = 
= 4400
Cost of plastering = Rs 4400
Q u e s t i o n : 9
The students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder
was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with carboard. If there were 35 competitors, how much cardboard was required to be bought for
the competition?
S o l u t i o n :
Q u e s t i o n : 1 0
The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.
S o l u t i o n :
Given that height h = 1.5 m
Diameter = 84 cm = 0.84 m
Radius = 
0.84
2
= 0. 42 m
Now, we have to find the area of the ground.
= 396 m
2
Cost of leveling for 1 m
2 
= 0.50
Cost of leveling for 396 m
2 
= ? Cost of leveling for 396 m
2 
= Rs.198
Q u e s t i o n : 1 1
Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of Rs
2.50 per square metre?
S o l u t i o n :
Page 5


Q u e s t i o n : 1
Curved surface area of a right circular cylinder is 4.4 m
2
. If the radius of the base of the cylinder is 0.7 m, find its height.
S o l u t i o n :
In the problem it is given that the Curved Surface Area of the cylinder is .
We know that,
Curved Surface Area of a cylinder 
Where,  radius of the cylinder and  height of the cylinder
In the given problem,  and h is to be found out.
Let us substitute all the given values in the formula for Curved Surface Area of the cylinder.
We have,
For simplifying the, this can be written as,
Now, clearly m
Therefore, the height of the cylinder is 1 meter.
Q u e s t i o n : 2
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
S o l u t i o n :
The following data is given in the problem:
h = 28 m
Diameter = 5 cm
We are asked to find the Total radiating surface, which is nothing but the Total Surface Area of the cylinder.
The height of the cylinder is in meters, so let us first convert it into centimeters.
h = 2800 cm
Also, the diameter of the cylinder is given, but we want the radius.
The formula for finding out the Total Surface Area is:
Total Surface Area
Substituting the above values in this equation, we have
Total Surface Area
Total Surface Area 
Total Surface Area 
Therefore, the answer to this problem is 
Q u e s t i o n : 3
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m
2
.
S o l u t i o n :
The data given in the problem is as follows:
Diameter of the cylinder =50cm
Height = 3.5m
Painting charges = Rs.12.50 per m
2
We have to find the total cost of painting the pillar
To find the cost of painting the pillar, we should first find the Curved Surface Area of the pillar using the given data.
Curved Surface Area 
r = 
Since the painting charges are given in terms of , we shall convert the radius from centimeters to meters.
r = 0.25m
Substituting the values in the formula for Curved Surface Area, we have
Curved Surface Area
Curved Surface Area = 5.5 m
2
It is given that, for 1 m
2 
the cost of painting is Rs.12.50
Therefore,
Total cost of painting the pillar = 
= 68.75
Therefore, the answer to this questions is, Rs.68.75
Q u e s t i o n : 4
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a  metal sheet. How many square metres of the sheet are required for the same?
S o l u t i o n :
The data given in the problem is as follows:
h = 1 m
Diameter = 140 cm
We are asked to find the area of the sheet in square meters required to make this cylinder.
Since it is a closed cylinder, the area of the sheet required to make this will be equal to the Total surface area of the cylinder.
Total surface area 
= =70cm
Since area is asked in square meters, let us convert the radius from centimeters to meters.
r = 0.7m
Substituting the values in the formula for the Total Surface Area of a cylinder, we have
Total Surface Area
Total Surface Area = 7.48
Therefore, the area of sheet required to make this cylinder is 7.48 square meters.
Q u e s t i o n : 5
The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.
S o l u t i o n :
Data given is the problem is as follows:
The cylinder is a hollow cylinder and is open on both sides
Total surface area of the cylinder is 4620 square centimeters
Area of the base ring = 115.5 square centimeters
Height = 7 cm
We are supposed to find the thickness of this cylinder.
We know that,
Total surface area of a hollow cylinder 
Where, r is the inner radius and R is the outer radius of the cylinder.
Now we have,
= 4620
Also, h = 7cm
= 4620
Also, it is given that
Area of base ring = 115.5
That is, = 115.5 …..
1
Substituting for in the above equation, we have
2
115.5 = 4620
=4389
Also, h = 7
Therefore,
.….
2
Now let us again take up equation
1
= 115.5
From equation
2 we have . Substitute this in the above equation.
(R – r) is nothing but the thickness of the cylinder.
Therefore, the thickness of the cylinder is cm
Q u e s t i o n : 6
Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.
S o l u t i o n :
Data given in the problem is as follows:
h =7.5 cm
r = 3.5 cm
We are supposed to find the ratio between the Total Surface Area and the Curved Surface Area.
We know that,
Total Surface Area
TSA = 
Curved Surface Area
CSA = 
Therefore,
= 
=
Substituting the values of h and r in the above expression, we have
= 
= = =
Hence the ratio between Total Surface area and Curved Surface Area is 22 : 15.
Q u e s t i o n : 7
A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 3.50 per
1000 cm
2
.
S o l u t i o n :
It is given that,
r = 70 cm
h = 1.4 m
Tin coating rate =  cm
2
We have to find the total cost of coating the cylinder with tin.
Let us first convert h from meters to centimeters.
h = 1.4 m
= 140 cm
Since the cylindrical vessel without lid has to be coated both on the inner side as well the outer side,
Area to be coated = 
=
= 154000 cm
2
Now let us find the total cost of coating this area.
For 1000 cm
2
 the cost of coating is Rs.3.50
For 154000 cm
2 
the cost of coating is given by =539
Therefore the total cost of coating the vessel on both inner and outer sides is Rs.539
Q u e s t i o n : 8
The inner diameter of a circular well is 3.5 m. It is 10 m deep Find:
i
inner curved surface area.
ii
the cost of plastering this curved surface at the rate of Rs 40 per m
2
.
S o l u t i o n :
Given data is as follows:
Inner diameter of the well = 3.5 m
h = 10 m
Rate of plastering = Rs.40 per square meter
We have to find two things,
1. Inner curved surface area
2. Total cost of plastering the inner curved surface
i
Inner curved surface area = 110
ii Now, let us find the total cost of plastering this area.
It is given that for 1 the cost of plastering is Rs.40
Therefore, for 110 the cost of plastering = 
= 4400
Cost of plastering = Rs 4400
Q u e s t i o n : 9
The students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder
was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with carboard. If there were 35 competitors, how much cardboard was required to be bought for
the competition?
S o l u t i o n :
Q u e s t i o n : 1 0
The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.
S o l u t i o n :
Given that height h = 1.5 m
Diameter = 84 cm = 0.84 m
Radius = 
0.84
2
= 0. 42 m
Now, we have to find the area of the ground.
= 396 m
2
Cost of leveling for 1 m
2 
= 0.50
Cost of leveling for 396 m
2 
= ? Cost of leveling for 396 m
2 
= Rs.198
Q u e s t i o n : 1 1
Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of Rs
2.50 per square metre?
S o l u t i o n :
Total cost of cleaning = Rs.314.28
Q u e s t i o n : 1 2
A solid cylinder has total surface area of 462 cm
2
. Its curved surface area is one-third of its total surface area. find the radius and height of the cylinder.
S o l u t i o n :
The data given in this problem is as follows:
Total Surface Area of the cylinder = 462 cm
2
Curved Surface Area
CSA = Total Surface Area
TSA
We have to find the radius and the height of the cylinder.
 
Using the given data, we have
Substituting the formula for Curved Surface Area and Total Surface Area in the above equation, we have
= 
= 
We have,
Total Surface Area = 462 cm
2
Substituting the formula for Total Surface Area in the above equation, we get
= 462
= 462
Now, we know that 
Substituting this in the above equation, we have
Since 
Therefore, the final answer to this question is,
Radius of the cylinder = 7cm
Height of the cylinder = 3.5cm