Surface Area and Volume of a Right Circular Cylinder- 2 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

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Q u e s t i o n : 1 5
A soft drink is available in two packs-i
a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and ii
a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
S o l u t i o n :
Given data is as follows:
i For tin can with rectangular base:
Length = 5 cm
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Q u e s t i o n : 1 5
A soft drink is available in two packs-i
a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and ii
a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
S o l u t i o n :
Given data is as follows:
i For tin can with rectangular base:
Length = 5 cm
Width = 4 cm
Height = 10 cm
ii For plastic cylinder with circular base
Diameter = 7 cm
Height = 10 cm
We have to find out which container has greater capacity and also the difference in their capacities.
i Volume of tin can = 
= 
=200 
ii Volume of cylinder = 
Diameter is given as 7cm. Therefore, r = 
Volume of cylinder = 
= 385 cm
3
From the above it can be concluded that plastic cylinder has greater capacity.
Difference in their capacities = 385 – 200 = 185 cm
3
Q u e s t i o n : 1 6
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such
pillars?
S o l u t i o n :
Given data is as follows:
Number of pillars = 14
We have to find the total amount of concrete present in all 14 pillars.
Radius of the pillar is given in centimeters, so let us convert it to meters.
Let us first find the amount of concrete present in one pillar, which is nothing but the volume of the pillar.
Therefore, total amount of concrete mixture in 14 pillars is 17.6 m
3
Q u e s t i o n : 1 7
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm
3
  of wood has a mass of 0.6
gm.
S o l u t i o n :
Given data is as follows:
Inner diameter = 24cm
Outer diameter = 28cm
h = 35cm
Mass of 1 cm
3
 of wood = 0.6gm
We have to find the mass of the pipe.
In this problem the inner and outer diameter of the pipe is given. Let us first find out the radius.
Inner radius (r) = 12cm
Outer radius (R) = 14cm
Volume of the hollow pipe = 
=
22
7
× 14
2
-12
2
×35 = 22 ×5 ×2 ×26
=5720 cm
3
It is given that,
1 cm
3 
of wood weighs 0.6gm
Therefore, 5720 of wood will weigh = 3432gm
= 3.432kg
Therefore, weight of the wooden pipe = 3.432kg
Q u e s t i o n : 1 8
( )
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Q u e s t i o n : 1 5
A soft drink is available in two packs-i
a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and ii
a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
S o l u t i o n :
Given data is as follows:
i For tin can with rectangular base:
Length = 5 cm
Width = 4 cm
Height = 10 cm
ii For plastic cylinder with circular base
Diameter = 7 cm
Height = 10 cm
We have to find out which container has greater capacity and also the difference in their capacities.
i Volume of tin can = 
= 
=200 
ii Volume of cylinder = 
Diameter is given as 7cm. Therefore, r = 
Volume of cylinder = 
= 385 cm
3
From the above it can be concluded that plastic cylinder has greater capacity.
Difference in their capacities = 385 – 200 = 185 cm
3
Q u e s t i o n : 1 6
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such
pillars?
S o l u t i o n :
Given data is as follows:
Number of pillars = 14
We have to find the total amount of concrete present in all 14 pillars.
Radius of the pillar is given in centimeters, so let us convert it to meters.
Let us first find the amount of concrete present in one pillar, which is nothing but the volume of the pillar.
Therefore, total amount of concrete mixture in 14 pillars is 17.6 m
3
Q u e s t i o n : 1 7
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm
3
  of wood has a mass of 0.6
gm.
S o l u t i o n :
Given data is as follows:
Inner diameter = 24cm
Outer diameter = 28cm
h = 35cm
Mass of 1 cm
3
 of wood = 0.6gm
We have to find the mass of the pipe.
In this problem the inner and outer diameter of the pipe is given. Let us first find out the radius.
Inner radius (r) = 12cm
Outer radius (R) = 14cm
Volume of the hollow pipe = 
=
22
7
× 14
2
-12
2
×35 = 22 ×5 ×2 ×26
=5720 cm
3
It is given that,
1 cm
3 
of wood weighs 0.6gm
Therefore, 5720 of wood will weigh = 3432gm
= 3.432kg
Therefore, weight of the wooden pipe = 3.432kg
Q u e s t i o n : 1 8
( )
If the lateral surface of a cylinder is 94.2 cm
2
 and its height is 5 cm, find:
i
radius of its base
ii
volume of the cylinder
[Use p
= 3.14]
S o l u t i o n :
Given data is as follows:
Lateral Surface Area = 94.2 cm
2
h = 5cm
We have to find:
i Radius of the base
ii Volume of the cylinder
i We know that,
Lateral Surface Area = 
That is,
2 prh = 94.2
=94.2
=94.2
ii Volume of a cylinder = 
=
Q u e s t i o n : 1 9
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
S o l u t i o n :
Given data is as follows:
Volume of the cylinder = 15.4 litres
h = 1m
We have to find the area of the sheet required to make this cylinder.
We know that 1 liter = 1000 cm
3
Therefore, 15.4 liters = 15400 cm
3
Also, h = 1m
=100cm
We know that,
Volume = 
Therefore,
=15400
Now, using this radius we have to find the Total Surface Area.
Total Surface Area = +
Q u e s t i o n : 2 0
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to
server 250 patients?
 
S o l u t i o n :
Given data is as follows:
Diameter = 7cm
h = 4cm
Number of patients = 250
We have to find the total volume of soup required to serve all 250 patients.
Given is the diameter, which is equal to 7cm. Therefore, 
Volume of soup given to each patient = 
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Q u e s t i o n : 1 5
A soft drink is available in two packs-i
a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and ii
a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
S o l u t i o n :
Given data is as follows:
i For tin can with rectangular base:
Length = 5 cm
Width = 4 cm
Height = 10 cm
ii For plastic cylinder with circular base
Diameter = 7 cm
Height = 10 cm
We have to find out which container has greater capacity and also the difference in their capacities.
i Volume of tin can = 
= 
=200 
ii Volume of cylinder = 
Diameter is given as 7cm. Therefore, r = 
Volume of cylinder = 
= 385 cm
3
From the above it can be concluded that plastic cylinder has greater capacity.
Difference in their capacities = 385 – 200 = 185 cm
3
Q u e s t i o n : 1 6
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such
pillars?
S o l u t i o n :
Given data is as follows:
Number of pillars = 14
We have to find the total amount of concrete present in all 14 pillars.
Radius of the pillar is given in centimeters, so let us convert it to meters.
Let us first find the amount of concrete present in one pillar, which is nothing but the volume of the pillar.
Therefore, total amount of concrete mixture in 14 pillars is 17.6 m
3
Q u e s t i o n : 1 7
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm
3
  of wood has a mass of 0.6
gm.
S o l u t i o n :
Given data is as follows:
Inner diameter = 24cm
Outer diameter = 28cm
h = 35cm
Mass of 1 cm
3
 of wood = 0.6gm
We have to find the mass of the pipe.
In this problem the inner and outer diameter of the pipe is given. Let us first find out the radius.
Inner radius (r) = 12cm
Outer radius (R) = 14cm
Volume of the hollow pipe = 
=
22
7
× 14
2
-12
2
×35 = 22 ×5 ×2 ×26
=5720 cm
3
It is given that,
1 cm
3 
of wood weighs 0.6gm
Therefore, 5720 of wood will weigh = 3432gm
= 3.432kg
Therefore, weight of the wooden pipe = 3.432kg
Q u e s t i o n : 1 8
( )
If the lateral surface of a cylinder is 94.2 cm
2
 and its height is 5 cm, find:
i
radius of its base
ii
volume of the cylinder
[Use p
= 3.14]
S o l u t i o n :
Given data is as follows:
Lateral Surface Area = 94.2 cm
2
h = 5cm
We have to find:
i Radius of the base
ii Volume of the cylinder
i We know that,
Lateral Surface Area = 
That is,
2 prh = 94.2
=94.2
=94.2
ii Volume of a cylinder = 
=
Q u e s t i o n : 1 9
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
S o l u t i o n :
Given data is as follows:
Volume of the cylinder = 15.4 litres
h = 1m
We have to find the area of the sheet required to make this cylinder.
We know that 1 liter = 1000 cm
3
Therefore, 15.4 liters = 15400 cm
3
Also, h = 1m
=100cm
We know that,
Volume = 
Therefore,
=15400
Now, using this radius we have to find the Total Surface Area.
Total Surface Area = +
Q u e s t i o n : 2 0
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to
server 250 patients?
 
S o l u t i o n :
Given data is as follows:
Diameter = 7cm
h = 4cm
Number of patients = 250
We have to find the total volume of soup required to serve all 250 patients.
Given is the diameter, which is equal to 7cm. Therefore, 
Volume of soup given to each patient = 
=
= 154 cm
3
Volume of soup for all 250 patients = 154 × 250
=38500 cm
3
We know that, 1000 cm
3 
= 1 litre.
Therefore,
Volume of soup for all 250 patients = 38.5 litres
Q u e s t i o n : 2 1
A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.
 
S o l u t i o n :
Given data is as follows:
h = 63 cm
Girth is nothing but the outer circumference of the roller, which is 440 cm.
Thickness of the roller = 4 cm
We have to find the volume of the roller.
We have been given the outer circumference of the roller. Let R be the external radius.
We have,
= 440
Also, thickness of the cylinder is given which is 4 cm. So we can easily find out the inner radius ‘r’.
Now, since we know both inner and outer radii, we can easily find out the volume of the hollow cylinder.
Volume = 
Q u e s t i o n : 2 2
The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs 198. The height of the tank is 6 times the radius of the base of the
tank. Find the volume corrected to 2 decimal places.
S o l u t i o n :
Data given is as follows:
Total cost of painting=Rs.198
Painting rate= Rs.0.50 per square decimeter
We have to find the volume of the cylinder.
We know that,
Total Surface Area of the cylinder =
2 prh +2 pr
2
Also, it is given that,
Total cost of painting = 198
That is,
= 198
2 prh +2 pr
2
×painting rate
=198
2 prh +2 pr
2
×0. 50
=198
2 prh +2 pr
2
= 396
In the above equation, let us replace with 6 .
=396
=396
( )
( )
( )
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Q u e s t i o n : 1 5
A soft drink is available in two packs-i
a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and ii
a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
S o l u t i o n :
Given data is as follows:
i For tin can with rectangular base:
Length = 5 cm
Width = 4 cm
Height = 10 cm
ii For plastic cylinder with circular base
Diameter = 7 cm
Height = 10 cm
We have to find out which container has greater capacity and also the difference in their capacities.
i Volume of tin can = 
= 
=200 
ii Volume of cylinder = 
Diameter is given as 7cm. Therefore, r = 
Volume of cylinder = 
= 385 cm
3
From the above it can be concluded that plastic cylinder has greater capacity.
Difference in their capacities = 385 – 200 = 185 cm
3
Q u e s t i o n : 1 6
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such
pillars?
S o l u t i o n :
Given data is as follows:
Number of pillars = 14
We have to find the total amount of concrete present in all 14 pillars.
Radius of the pillar is given in centimeters, so let us convert it to meters.
Let us first find the amount of concrete present in one pillar, which is nothing but the volume of the pillar.
Therefore, total amount of concrete mixture in 14 pillars is 17.6 m
3
Q u e s t i o n : 1 7
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm
3
  of wood has a mass of 0.6
gm.
S o l u t i o n :
Given data is as follows:
Inner diameter = 24cm
Outer diameter = 28cm
h = 35cm
Mass of 1 cm
3
 of wood = 0.6gm
We have to find the mass of the pipe.
In this problem the inner and outer diameter of the pipe is given. Let us first find out the radius.
Inner radius (r) = 12cm
Outer radius (R) = 14cm
Volume of the hollow pipe = 
=
22
7
× 14
2
-12
2
×35 = 22 ×5 ×2 ×26
=5720 cm
3
It is given that,
1 cm
3 
of wood weighs 0.6gm
Therefore, 5720 of wood will weigh = 3432gm
= 3.432kg
Therefore, weight of the wooden pipe = 3.432kg
Q u e s t i o n : 1 8
( )
If the lateral surface of a cylinder is 94.2 cm
2
 and its height is 5 cm, find:
i
radius of its base
ii
volume of the cylinder
[Use p
= 3.14]
S o l u t i o n :
Given data is as follows:
Lateral Surface Area = 94.2 cm
2
h = 5cm
We have to find:
i Radius of the base
ii Volume of the cylinder
i We know that,
Lateral Surface Area = 
That is,
2 prh = 94.2
=94.2
=94.2
ii Volume of a cylinder = 
=
Q u e s t i o n : 1 9
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
S o l u t i o n :
Given data is as follows:
Volume of the cylinder = 15.4 litres
h = 1m
We have to find the area of the sheet required to make this cylinder.
We know that 1 liter = 1000 cm
3
Therefore, 15.4 liters = 15400 cm
3
Also, h = 1m
=100cm
We know that,
Volume = 
Therefore,
=15400
Now, using this radius we have to find the Total Surface Area.
Total Surface Area = +
Q u e s t i o n : 2 0
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to
server 250 patients?
 
S o l u t i o n :
Given data is as follows:
Diameter = 7cm
h = 4cm
Number of patients = 250
We have to find the total volume of soup required to serve all 250 patients.
Given is the diameter, which is equal to 7cm. Therefore, 
Volume of soup given to each patient = 
=
= 154 cm
3
Volume of soup for all 250 patients = 154 × 250
=38500 cm
3
We know that, 1000 cm
3 
= 1 litre.
Therefore,
Volume of soup for all 250 patients = 38.5 litres
Q u e s t i o n : 2 1
A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.
 
S o l u t i o n :
Given data is as follows:
h = 63 cm
Girth is nothing but the outer circumference of the roller, which is 440 cm.
Thickness of the roller = 4 cm
We have to find the volume of the roller.
We have been given the outer circumference of the roller. Let R be the external radius.
We have,
= 440
Also, thickness of the cylinder is given which is 4 cm. So we can easily find out the inner radius ‘r’.
Now, since we know both inner and outer radii, we can easily find out the volume of the hollow cylinder.
Volume = 
Q u e s t i o n : 2 2
The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs 198. The height of the tank is 6 times the radius of the base of the
tank. Find the volume corrected to 2 decimal places.
S o l u t i o n :
Data given is as follows:
Total cost of painting=Rs.198
Painting rate= Rs.0.50 per square decimeter
We have to find the volume of the cylinder.
We know that,
Total Surface Area of the cylinder =
2 prh +2 pr
2
Also, it is given that,
Total cost of painting = 198
That is,
= 198
2 prh +2 pr
2
×painting rate
=198
2 prh +2 pr
2
×0. 50
=198
2 prh +2 pr
2
= 396
In the above equation, let us replace with 6 .
=396
=396
( )
( )
( )
=396
=3 decimeters
= =18 decimeters
Volume of the cylinder = 
Q u e s t i o n : 2 3
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes and the ratio of their curved surfaces.
S o l u t i o n :
Data given is as follows:
Ratio of radii of two cylinders = 2:3
Ratio of heights of two cylinders = 5:3
We have to find out the following:
i Ratio of the volumes of the two cylinders
ii Ratio of the Curved Surface Area of the two cylinders
Let and be the radii of the two cylinders respectively.
Let  and be the heights of the two cylinders respectively.
Therefore we have,
i Since we have to find the ratio of the volumes of the two cylinders, we have
ii Since we have to find the ratio of the curved surface areas of the two cylinders, we have,
=
Q u e s t i o n : 2 4
The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm
2
.
S o l u t i o n :
Data given is as follows:
We have to find the volume of the cylinder.
From the given data we have,
Also,