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CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 7 - MCQExams.com
CBSE
Class 9 Maths
Surface Areas And Volumes
Quiz 7
The side of the base of a dice is
5.5
mm. Find the surface area of a dice whose edges are squares.
Report Question
0%
181.5
m
m
2
0%
90.21
m
m
2
0%
180.2
m
m
2
0%
120.4
m
m
2
Explanation
Given, side of base
=
5.5
mm
Total surface area of a cube
=
6
×
side
2
=
6
×
5.5
×
5.5
=
181.5
m
m
2
Find the surface area of a cube with side
12
m
Report Question
0%
814
m
2
0%
864
m
2
0%
854
m
2
0%
841
m
2
Explanation
Total surface area of a cube
=
6
×
side
2
=
6
×
12
×
12
=
864
m
2
A cubical water tank measures
3
feet sides. Find its surface area.
Report Question
0%
9
f
t
2
0%
50
f
t
2
0%
52
f
t
2
0%
54
f
t
2
Explanation
S
u
r
f
a
c
e
a
r
e
a
o
f
a
c
u
b
e
=
6
×
S
i
d
e
2
s
i
d
e
=
3
f
t
S
u
r
f
a
c
e
A
r
e
a
=
6
×
3
2
S
u
r
f
a
c
e
A
r
e
a
=
6
×
9
S
u
r
f
a
c
e
A
r
e
a
=
54
f
t
2
The length of the side is
3.9
ft. Find the surface area of a cube .
Report Question
0%
41.82
f
t
2
0%
94.16
f
t
2
0%
91.26
f
t
2
0%
40.41
f
t
2
Explanation
Given, length of side
=
.9
ft
Total surface area of a cube
=
6
×
side
2
=
6
×
3.9
×
3.9
=
91.26
f
t
2
The curved surface of a cylinder is
1000
m
m
2
and the radius is
20
mm. Find height of the cylinder. (Round off the answer to nearest whole number).
Report Question
0%
8
m
m
0%
9
m
m
0%
7.9
m
m
0%
7.96
m
m
Explanation
Curved surface area of cylinder is
A
=
2
π
r
h
Here, the curved surface area is
A
=
1000
mm
2
the radius is
r
=
20
mm.
Thus,
A
=
2
π
r
h
⇒
1000
=
2
×
22
7
×
20
×
h
⇒
1000
×
7
=
2
×
22
×
20
×
h
⇒
7000
=
880
×
h
⇒
h
=
7000
880
=
7.96
Hence, height
of the cylinder is
7.96
m
m
.
The curved surface area of the cylinder is
2
π
r
h
where as surface area of the cylinder is
Report Question
0%
π
r
(
r
+
h
)
0%
π
r
l
(
r
+
h
)
0%
2
π
r
(
r
+
h
)
0%
2
π
r
2
l
(
r
+
h
)
Explanation
The curved surface area of the cylinder is
2
π
r
h
where as surface area of the cylinder is
2
π
r
(
r
+
h
)
.
Surface area includes curved surface area and two circular bases of the cylinder.
The diameter of a cylinder is
12
m and its height is
10
m. Find the curved surface area of a cylinder.
Report Question
0%
240
π
c
m
2
0%
120
π
m
2
0%
220
π
m
2
0%
230
π
m
m
2
Explanation
Curved surface area of cylinder is
A
=
2
π
r
h
Here, the diameter is
12
m and therefore, the radius is half of diameter that is
r
=
6
m and height is
10
m.
Thus,
A
=
2
π
r
h
=
2
×
π
×
6
×
10
=
120
π
m
2
Hence, the c
urved surface area
of the cylinder is
120
π
m
2
.
Choose the correct formula for surface area of a cylinder.
Report Question
0%
2
π
r
2
+
2
π
r
h
0%
π
r
2
+
π
r
h
0%
2
π
r
+
2
π
r
h
0%
2
π
r
2
+
π
r
h
Explanation
A cylinder comprises two circles and one rectangle as given in the figure
The surface area of a circle is
π
r
2
where
r
is the radius and the surface area of a rectangle is
2
π
r
h
.
⟹
Surface area of cylinder
=
2
×
area of the circular base
+
area of the rectangle
⇒
Surface area of cylinder
=
2
π
r
2
+
2
π
r
h
Find the area of the curved surface of a cylindrical box with radius 12 inches and height 20 inches.
Report Question
0%
1505.1
i
n
2
0%
1506.5
i
n
2
0%
1507.5
i
n
2
0%
1507.2
i
n
2
Explanation
Curved surface area of cylinder is
A
=
2
π
r
h
Here, the radius is
12
in and height is
20
in.
Thus,
A
=
2
π
r
h
=
2
×
3.14
×
12
×
20
=
1507.2
in
2
Hence, the c
urved surface area
of the cylinder is
1507.2
in
2
.
Find the surface area of the cylinder shown above:
Report Question
0%
0.46
π
0%
0.46
π
m
3
0%
0.46
π
m
2
0%
0.46
π
c
m
Explanation
Given: Radius of cylinder
r
=
0.1
m
and Height
h
=
2.2
m
.
Surface area of a cylinder =
2
π
r
(
r
+
h
)
=
2
×
π
×
0.1
(
0.1
+
2.2
)
=
2
×
π
×
0.1
(
2.3
)
=
0.46
π
m
2
So, option C is correct.
Find the surface area of a cylinder:
r
=
9
i
n
,
h
=
18
i
n
Report Question
0%
1526.04
i
n
2
0%
1525.03
i
n
2
0%
1526.04
i
n
0%
1526.04
i
n
3
Explanation
Surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Here, radius is
r
=
9
in and the height is
h
=
18
in.
Thus,
A
=
2
π
r
(
r
+
h
)
=
2
×
3.14
×
9
(
9
+
18
)
=
56.52
×
27
=
1526.04
Hence, the surface area
of the cylinder is
1526.04
in
2
.
The volume of a cylinder is
616
cubic feet and height
4
feet. Find its curved surface area. (Use
π
=
22
/
7
)
Report Question
0%
88
f
t
2
0%
198
f
t
2
0%
79
f
t
2
0%
176
f
t
2
Explanation
Volume of a cylinder
=
π
r
2
h
⇒
616
=
22
7
×
r
2
×
4
⇒
616
×
7
22
×
4
=
r
2
⇒
r
2
=
49
⇒
r
=
√
49
=
7
f
t
Curved surface area
=
2
π
r
h
=
2
×
22
7
×
7
×
4
=
176
square feet
The inner radius of a cylindrical wooden furniture is
8
m and its outer radius is
12
m. The height of the furniture is
35
m. Find its lateral surface area. (Use
π
=
22
/
7
).
Report Question
0%
880
m
3
0%
880
m
2
0%
88
m
2
0%
880
m
m
2
Explanation
Given: Inner radius of the cylindrical furniture (r)
=
8
m
Outer radius of the cylindrical furniture (R)
=
12
m
Height of the furniture (h)
=
35
m
∴
Lateral Surface area
=
2
π
(
R
−
r
)
h
=
2
×
22
7
×
(
12
−
8
)
×
35
=
2
×
22
×
4
×
5
=
880
m
2
If the lateral surface of a cylinder is
500
c
m
2
and ts height is
10
c
m
, then find radius of its base. (use
π
=
3.14
).
Report Question
0%
6.92
c
m
0%
7.96
c
m
0%
6.54
c
m
0%
8.22
c
m
Explanation
Here, the lateral surface area is
A
=
500
c
m
2
and the height is
h
=
10
c
m
Let, the radius be
r
Lateral surface area of cylinder is
A
=
2
π
r
h
Thus,
A
=
2
π
r
h
⇒
500
=
2
×
3.14
×
r
×
10
⇒
500
=
62.8
r
⇒
r
=
500
62.8
=
7.96
Hence, radius
of the cylinder is
7.96
c
m
.
The circumference of a circle is
200
feet and height is
12
feet. Find its curved surface area of a cylinder.
Report Question
0%
2400
f
t
2
0%
2100
f
t
2
0%
2300
f
t
2
0%
2010
f
t
2
Explanation
Circumference of cylinder is
C
=
2
π
r
It is given that the circumference is
200
feet, therefore,
C
=
2
π
r
⇒
200
=
2
π
r
⇒
r
=
200
2
π
=
100
π
Now, curved surface area of cylinder is
A
=
2
π
r
h
Here, the radius is
100
π
ft and height is
12
ft.
Thus,
A
=
2
π
r
h
=
2
π
×
100
π
×
12
=
2
×
100
×
12
=
2400
ft
2
Hence, the c
urved surface area
of the cylinder is
2400
ft
2
.
David built a recycling cylindrical bin that is 12 feet long and its base is 56 feet radius. Find the surface area of the bin.
Report Question
0%
23936
f
t
3
0%
23936
f
t
2
0%
23950
f
t
2
0%
23936
f
t
Explanation
Surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Here the cylindrical bin has radius
r
=
56
ft and height
h
=
12
ft.
Thus,
A
=
2
π
r
(
r
+
h
)
=
2
×
3.14
×
56
(
56
+
12
)
=
351.68
×
68
=
23936.24
Hence, the surface area
of the cylindrical bin is approximately equal to
23936
ft
2
.
Find the curved surface area of the cylinder given above:
Report Question
0%
1507.2
m
2
0%
1527.6
m
2
0%
1517.8
m
2
0%
1588.1
m
3
Explanation
Given,
Height
h
=
40
m
Diameter =
12
m
Radius
r
=
D
i
a
m
e
t
e
r
2
=
12
2
m
=
6
m
Curved surface area
=
2
π
r
h
=
2
×
3.14
×
6
×
40
m
2
=
1507.2
m
2
So, option A is correct.
The radius of the base of a cylinder is 20 cm and the height is 12 cm. Find the surface area of the cylinder. (Assume
π
=
3.14
).
Report Question
0%
4019.2
c
m
3
0%
4019.2
c
m
0%
4019.2
c
m
2
0%
4018.6
c
m
2
Explanation
Surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Here, radius is
r
=
20
cm and the height is
h
=
12
cm.
Thus,
A
=
2
π
r
(
r
+
h
)
=
2
×
3.14
×
20
(
20
+
12
)
=
125.6
×
32
=
4019.2
Hence, the surface area
of the cylinder is
4019.2
c
m
2
.
Find the height of a cylinder that has a diameter of
10
feet and a surface area of
220
f
t
2
. Round your answer to the nearest whole number.
(use
π
=
22
/
7
).
Report Question
0%
0.1
ft
0%
3
ft
0%
2
ft
0%
1
ft
Explanation
Surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Here the cylinder has surface area
A
=
220
ft
2
and diameter
10
ft and therefore, the radius is half of the diameter that is
r
=
5
ft.
Thus,
A
=
2
π
r
(
r
+
h
)
⇒
220
=
2
×
22
7
×
5
(
5
+
h
)
⇒
220
=
44
7
(
25
+
5
h
)
⇒
220
×
7
=
1100
+
220
h
⇒
1540
−
1100
=
220
h
⇒
220
h
=
440
⇒
h
=
440
220
=
2
Hence, the height
of the cylinder is
2
ft
.
A cylindrical drum has its height 20 inches and curved surface area as
200
i
n
2
. Find surface area of cylindrical drum.(
π
=
22
/
7
)
Report Question
0%
203.5
i
n
2
0%
207.3
i
n
2
0%
215.7
i
n
2
0%
218.13
Judah wants to make a cylindrical drum that will fit a bass with a height
15
in. and a diameter of
48
in. What is the surface area of the drum?
Take
π
=
3.14
Report Question
0%
5810.10
i
n
0%
5810.10
i
n
2
0%
5878.08
i
n
2
0%
5878
i
n
2
Explanation
Surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Here, diameter is
48
in and therefore, the radius is half of diameter that is
r
=
24
in and the height is
h
=
15
in.
Thus,
A
=
2
π
r
(
r
+
h
)
=
2
×
3.14
×
24
(
24
+
15
)
=
150.72
×
39
=
5878.08
Hence, the surface area
of the cylindrical drum is
5878.08
in
2
.
Edward bought a container of ceralac in the shape of cylinder. If the container has a radius
10
m
and a surface area is
340
π
. What is its height?
Report Question
0%
5
m
0%
6
m
0%
7
m
0%
8
m
Explanation
Surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Here the cylindrical container has surface area
A
=
340
π
m
2
and radius
r
=
10
m.
Thus,
A
=
2
π
r
(
r
+
h
)
⇒
340
π
=
2
π
×
10
(
10
+
h
)
⇒
340
π
=
20
π
(
10
+
h
)
⇒
340
π
=
200
π
+
20
π
h
⇒
20
π
h
=
340
π
−
200
π
⇒
20
π
h
=
140
π
⇒
h
=
140
π
20
π
=
7
Hence, the height
of the cylindrical container is
7
m
.
Find the total surface area of the cylinder. (Use
π
=
3.14
).
Report Question
0%
678.99
f
t
2
0%
3881.05
f
t
2
0%
3881.04
f
t
0%
678.24
f
t
2
Explanation
Given:
r
=
6
f
t
and
h
=
12
f
t
The total surface area of a cylinder =
2
π
r
(
r
+
h
)
=
2
×
3.14
×
6
(
6
+
12
)
=
2
×
3.14
×
6
(
18
)
=
678.24
f
t
2
So, option D is correct.
The surface area of a cylindrical box is
132
m
m
2
and its height is
4
m
m
.
Find its radius.
Report Question
0%
2
m
m
0%
3
m
m
0%
4
m
m
0%
5
m
m
Explanation
Given: Cylindrical box has surface area
A
=
132
m
m
2
and height
h
=
4
m
m
We know surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Thus,
132
=
2
×
22
7
×
r
(
r
+
4
)
⇒
132
=
44
7
r
(
r
+
4
)
⇒
132
×
7
=
44
r
(
r
+
4
)
⇒
924
=
44
r
2
+
176
r
⇒
44
r
2
+
176
r
−
924
=
0
⇒
r
2
+
4
r
−
21
=
0
⇒
r
2
+
7
r
−
3
r
−
21
=
0
⇒
r
(
r
+
7
)
−
3
(
r
+
7
)
=
0
⇒
r
+
7
=
0
,
r
−
3
=
0
⇒
r
=
−
7
,
r
=
3
Hence, the radius
of the cylindrical box is
3
mm
.
A skating board rocks back and forth on a wooden cylinder. The cylinder has a radius of 6 inches and a surface area is
590
i
n
2
. Find the height of the cylinder. (
π
=
3.14
).
Report Question
0%
10
in
0%
9.65
in
0%
9
in
0%
9.5
in
Explanation
Surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Here the wooden cylinder has surface area
A
=
590
in
2
and radius
r
=
6
mm.
Thus,
A
=
2
π
r
(
r
+
h
)
⇒
590
=
2
×
22
7
×
6
(
6
+
h
)
⇒
590
=
44
7
(
36
+
6
h
)
⇒
590
×
7
=
1584
+
264
h
⇒
4130
−
1584
=
264
h
⇒
264
h
=
2546
⇒
h
=
2546
264
=
9.643
Hence, the height
of the wooden cylinder is
9.65
in
.
Find the volume of the hemisphere with radius
6
cm.
Report Question
0%
352.16
c
m
3
0%
452.16
c
m
3
0%
252.16
c
m
3
0%
152.16
c
m
3
Explanation
Given, radius of hemisphere
=
6
cm
Volume of the hemisphere
=
2
3
π
r
3
=
2
3
×
3.14
×
6
3
=
452.16
c
m
3
A gas cylinder has a diameter of
14
m and height is
0.2
m. Find its surface area. (
π
=
22
/
7
)
Report Question
0%
316.512
m
m
2
0%
316.512
m
0%
316.512
m
3
0%
316.512
m
2
Explanation
Surface area of cylinder is
A
=
2
π
r
(
r
+
h
)
Here the gas cylinder has diameter
14
m and therefore, the radius is half of diameter that is
r
=
7
m and height
h
=
0.2
m.
Thus,
A
=
2
π
r
(
r
+
h
)
=
2
×
22
7
×
7
(
7
+
0.2
)
=
316.512
Hence, the surface area
of the gas cylinder is
316.512
m
2
.
The curved surface area of a cylinder is
188.4
m
2
. The height is
12
m
. What is the radius? (use
π
=
3.14
).
Report Question
0%
2
c
m
0%
2.5
c
m
0%
2
m
0%
2.5
m
Explanation
Curved surface area of cylinder is
A
=
2
π
r
h
Here, the curved surface area is
A
=
188.4
m
2
the height is
h
=
12
m
.
Thus,
A
=
2
π
r
h
⇒
188.4
=
2
×
3.14
×
r
×
12
⇒
188.4
=
75.36
r
⇒
r
=
188.4
75.36
=
2.5
Hence, radius
of the cylinder is
2.5
m
Find the volume of a sphere whose diameter is
7.2
m
m
.
Report Question
0%
195.33
m
3
0%
175.33
m
m
3
0%
195.33
m
m
3
0%
185.33
m
m
3
Explanation
Formula:
Volume of sphere
=
4
3
π
r
3
r
=
r
a
d
i
u
s
Given:
d
i
a
m
e
t
e
r
(
d
)
=
7.2
m
m
r
a
d
i
u
s
(
r
)
=
d
2
=
7.2
2
=
3.6
m
m
⇒
4
3
π
r
3
=
4
3
×
3.14
×
(
3.6
)
3
=
4
3
×
3.6
×
3.6
×
3.6
×
3.14
=
4
3
×
46.656
t
i
m
e
s
3.14
=
585.999
3
=
195.33
m
m
3
What is the volume of a sphere? (use
π
=
3.14
)
Report Question
0%
6
,
878.82
i
n
3
0%
6
,
578.82
i
n
3
0%
5
,
878.82
i
n
3
0%
6
,
808.82
i
n
3
Explanation
Formula:
Volume of sphere
=
4
3
π
r
3
where,
r
=
r
a
d
i
u
s
Given:
r
=
11.8
After substituting the values in the formula we
4
3
π
r
3
=
4
3
×
3.14
×
11.8
3
=
4
3
×
3.14
×
11.8
×
11.8
×
11.8
=
20636.481
3
=
6878.82
i
n
3
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