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

 Page 1


Q u e s t i o n : 5 1
Mark the correct alternative in each of the following:
In a cylinder, if radius is doubled and height is halved, curved surface area will be
a
halved
b
doubled
c
same
d
four times
S o l u t i o n :
Let S
1
 be the curved surface area of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let S
2
 be the surface area after changing the dimension, then
So,
Hence, the correct option is
c
Q u e s t i o n : 5 2
Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is
a
1 : 4
b
1 : 3
c
3 : 1
d
2 : 5
S o l u t i o n :
Let V
1
 and V
2
 be the volume of the two cylinders with radius r
1
 and height h
1
, and radius r
2
 and height h
2
, where 
So,
 …….
1
Now,
 ……
2
From equation
1 and
2, we have
Hence, the correct option is
c
Q u e s t i o n : 5 3
The number of surfaces in right cylinder is
a
1
b
2
c
3
d
4
Page 2


Q u e s t i o n : 5 1
Mark the correct alternative in each of the following:
In a cylinder, if radius is doubled and height is halved, curved surface area will be
a
halved
b
doubled
c
same
d
four times
S o l u t i o n :
Let S
1
 be the curved surface area of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let S
2
 be the surface area after changing the dimension, then
So,
Hence, the correct option is
c
Q u e s t i o n : 5 2
Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is
a
1 : 4
b
1 : 3
c
3 : 1
d
2 : 5
S o l u t i o n :
Let V
1
 and V
2
 be the volume of the two cylinders with radius r
1
 and height h
1
, and radius r
2
 and height h
2
, where 
So,
 …….
1
Now,
 ……
2
From equation
1 and
2, we have
Hence, the correct option is
c
Q u e s t i o n : 5 3
The number of surfaces in right cylinder is
a
1
b
2
c
3
d
4
S o l u t i o n :
In a cylinder there are three surfaces, one is curved surface area and other two are circular discs.
Hence, the correct option is
c
Q u e s t i o n : 5 4
Vertical cross-section of a right circular cylinder is always a
a
square
b
rectangle
c
rhombus
d
trapezium
S o l u t i o n :
From the following figure of cylinder we observe that the vertical cross section is the rectangle PQRS.
Hence, the correct option is
b
Q u e s t i o n : 5 5
If r is the radius and h is height of the cylinder the volume will be
a
1
3
pr
2
h
b
pr
2
h
c
2 pr (h + r)
d
2 prh
S o l u t i o n :
It is given that r is the radius and h is the height of the cylinder.
We know that the volume of cylinder is given by the formula
Hence, the correct option is
b
Q u e s t i o n : 5 6
The number of surfaces of a hollow cylindrical object is
a
1
b
2
c
3
Page 3


Q u e s t i o n : 5 1
Mark the correct alternative in each of the following:
In a cylinder, if radius is doubled and height is halved, curved surface area will be
a
halved
b
doubled
c
same
d
four times
S o l u t i o n :
Let S
1
 be the curved surface area of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let S
2
 be the surface area after changing the dimension, then
So,
Hence, the correct option is
c
Q u e s t i o n : 5 2
Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is
a
1 : 4
b
1 : 3
c
3 : 1
d
2 : 5
S o l u t i o n :
Let V
1
 and V
2
 be the volume of the two cylinders with radius r
1
 and height h
1
, and radius r
2
 and height h
2
, where 
So,
 …….
1
Now,
 ……
2
From equation
1 and
2, we have
Hence, the correct option is
c
Q u e s t i o n : 5 3
The number of surfaces in right cylinder is
a
1
b
2
c
3
d
4
S o l u t i o n :
In a cylinder there are three surfaces, one is curved surface area and other two are circular discs.
Hence, the correct option is
c
Q u e s t i o n : 5 4
Vertical cross-section of a right circular cylinder is always a
a
square
b
rectangle
c
rhombus
d
trapezium
S o l u t i o n :
From the following figure of cylinder we observe that the vertical cross section is the rectangle PQRS.
Hence, the correct option is
b
Q u e s t i o n : 5 5
If r is the radius and h is height of the cylinder the volume will be
a
1
3
pr
2
h
b
pr
2
h
c
2 pr (h + r)
d
2 prh
S o l u t i o n :
It is given that r is the radius and h is the height of the cylinder.
We know that the volume of cylinder is given by the formula
Hence, the correct option is
b
Q u e s t i o n : 5 6
The number of surfaces of a hollow cylindrical object is
a
1
b
2
c
3
d
4
S o l u t i o n :
In a hollow cylinder, there are two curved surface areas: inner and outer and one circular base with inner and outer surface area.
Hence, the correct option is
d
Q u e s t i o n : 5 7
If the radius of a cylinder is doubled and the height remains same, the volume will be
a
doubled
b
halved
c
same
d
four times
S o l u t i o n :
Let V
1
 be the volume of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let V
2
 be the volume after changing the dimension, then
So,
Hence, the correct option is
d
Q u e s t i o n : 5 8
If the height of a cylinder is doubled and radius remains the same, then volume will be
a
doubled
b
halved
c
same
d
four times
S o l u t i o n :
Let V
1
 be the volume of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let V
2
 be the volume after changing the dimension, then
So,
Hence, the correct option is
Page 4


Q u e s t i o n : 5 1
Mark the correct alternative in each of the following:
In a cylinder, if radius is doubled and height is halved, curved surface area will be
a
halved
b
doubled
c
same
d
four times
S o l u t i o n :
Let S
1
 be the curved surface area of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let S
2
 be the surface area after changing the dimension, then
So,
Hence, the correct option is
c
Q u e s t i o n : 5 2
Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is
a
1 : 4
b
1 : 3
c
3 : 1
d
2 : 5
S o l u t i o n :
Let V
1
 and V
2
 be the volume of the two cylinders with radius r
1
 and height h
1
, and radius r
2
 and height h
2
, where 
So,
 …….
1
Now,
 ……
2
From equation
1 and
2, we have
Hence, the correct option is
c
Q u e s t i o n : 5 3
The number of surfaces in right cylinder is
a
1
b
2
c
3
d
4
S o l u t i o n :
In a cylinder there are three surfaces, one is curved surface area and other two are circular discs.
Hence, the correct option is
c
Q u e s t i o n : 5 4
Vertical cross-section of a right circular cylinder is always a
a
square
b
rectangle
c
rhombus
d
trapezium
S o l u t i o n :
From the following figure of cylinder we observe that the vertical cross section is the rectangle PQRS.
Hence, the correct option is
b
Q u e s t i o n : 5 5
If r is the radius and h is height of the cylinder the volume will be
a
1
3
pr
2
h
b
pr
2
h
c
2 pr (h + r)
d
2 prh
S o l u t i o n :
It is given that r is the radius and h is the height of the cylinder.
We know that the volume of cylinder is given by the formula
Hence, the correct option is
b
Q u e s t i o n : 5 6
The number of surfaces of a hollow cylindrical object is
a
1
b
2
c
3
d
4
S o l u t i o n :
In a hollow cylinder, there are two curved surface areas: inner and outer and one circular base with inner and outer surface area.
Hence, the correct option is
d
Q u e s t i o n : 5 7
If the radius of a cylinder is doubled and the height remains same, the volume will be
a
doubled
b
halved
c
same
d
four times
S o l u t i o n :
Let V
1
 be the volume of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let V
2
 be the volume after changing the dimension, then
So,
Hence, the correct option is
d
Q u e s t i o n : 5 8
If the height of a cylinder is doubled and radius remains the same, then volume will be
a
doubled
b
halved
c
same
d
four times
S o l u t i o n :
Let V
1
 be the volume of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let V
2
 be the volume after changing the dimension, then
So,
Hence, the correct option is
a
Q u e s t i o n : 5 9
In a cylinder, if radius is halved and height is doubled, the volume will be
a
same
b
doubled
c
halved
d
four times
S o l u t i o n :
Let V
1
 be the volume of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let V
2
 be the volume after changing the dimension, then
So,
Hence, the correct option is
c
Q u e s t i o n : 6 0
If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is
a
2 ph
2
b
3
2
ph
2
c
4
3
ph
2
d
ph
2
S o l u t i o n :
Let r be the radius of the cylinder and h be its height.
It is given that:
Therefore, total surface area S is:
Hence, the correct option is
b
Q u e s t i o n : 6 1
A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m
2
, is
a
40 p
b
80 p
c
160 p
d
Page 5


Q u e s t i o n : 5 1
Mark the correct alternative in each of the following:
In a cylinder, if radius is doubled and height is halved, curved surface area will be
a
halved
b
doubled
c
same
d
four times
S o l u t i o n :
Let S
1
 be the curved surface area of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let S
2
 be the surface area after changing the dimension, then
So,
Hence, the correct option is
c
Q u e s t i o n : 5 2
Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is
a
1 : 4
b
1 : 3
c
3 : 1
d
2 : 5
S o l u t i o n :
Let V
1
 and V
2
 be the volume of the two cylinders with radius r
1
 and height h
1
, and radius r
2
 and height h
2
, where 
So,
 …….
1
Now,
 ……
2
From equation
1 and
2, we have
Hence, the correct option is
c
Q u e s t i o n : 5 3
The number of surfaces in right cylinder is
a
1
b
2
c
3
d
4
S o l u t i o n :
In a cylinder there are three surfaces, one is curved surface area and other two are circular discs.
Hence, the correct option is
c
Q u e s t i o n : 5 4
Vertical cross-section of a right circular cylinder is always a
a
square
b
rectangle
c
rhombus
d
trapezium
S o l u t i o n :
From the following figure of cylinder we observe that the vertical cross section is the rectangle PQRS.
Hence, the correct option is
b
Q u e s t i o n : 5 5
If r is the radius and h is height of the cylinder the volume will be
a
1
3
pr
2
h
b
pr
2
h
c
2 pr (h + r)
d
2 prh
S o l u t i o n :
It is given that r is the radius and h is the height of the cylinder.
We know that the volume of cylinder is given by the formula
Hence, the correct option is
b
Q u e s t i o n : 5 6
The number of surfaces of a hollow cylindrical object is
a
1
b
2
c
3
d
4
S o l u t i o n :
In a hollow cylinder, there are two curved surface areas: inner and outer and one circular base with inner and outer surface area.
Hence, the correct option is
d
Q u e s t i o n : 5 7
If the radius of a cylinder is doubled and the height remains same, the volume will be
a
doubled
b
halved
c
same
d
four times
S o l u t i o n :
Let V
1
 be the volume of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let V
2
 be the volume after changing the dimension, then
So,
Hence, the correct option is
d
Q u e s t i o n : 5 8
If the height of a cylinder is doubled and radius remains the same, then volume will be
a
doubled
b
halved
c
same
d
four times
S o l u t i o n :
Let V
1
 be the volume of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let V
2
 be the volume after changing the dimension, then
So,
Hence, the correct option is
a
Q u e s t i o n : 5 9
In a cylinder, if radius is halved and height is doubled, the volume will be
a
same
b
doubled
c
halved
d
four times
S o l u t i o n :
Let V
1
 be the volume of the cylinder with radius r
1
 and height h
1
, then
 …….
1
Now, let V
2
 be the volume after changing the dimension, then
So,
Hence, the correct option is
c
Q u e s t i o n : 6 0
If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is
a
2 ph
2
b
3
2
ph
2
c
4
3
ph
2
d
ph
2
S o l u t i o n :
Let r be the radius of the cylinder and h be its height.
It is given that:
Therefore, total surface area S is:
Hence, the correct option is
b
Q u e s t i o n : 6 1
A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m
2
, is
a
40 p
b
80 p
c
160 p
d
200 p
S o l u t i o n :
Let r be the radius of the cylinder and h be its height.
It is given that:
And,
Therefore, total surface area S of the sheet required is:
Hence, the correct option is
b
Q u e s t i o n : 6 2
Two circular cylinders of equal volume have their heights in the ratio 1 : 2 Ratio of their radii is
a
1 : v 2
b
v 2: 1
c
1 : 2
d
1 : 4
d
S o l u t i o n :
Let V
1
 and V
2
 be the volume of the two cylinders with h
1
 and h
2
 as their heights:
Let r
1
 and r
2
 be their base radius.
It is given that
Hence, the correct option is
b
Q u e s t i o n : 6 3
The radius of a wire is decreased to one-third. If volume remains the same, the length will become
a
3 times
b
6 times
c
9 times
d
27 times
S o l u t i o n :
Let V
1
 and V
2
 be the volume of the two cylinders with h
1
 and h
2
 as their heights:
Let r
1
 and r
2
 be their base radius.
It is given that
Hence, the length will become 9 times.
Hence, the correct option is
c
Q u e s t i o n : 6 4
If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?