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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=2πrh
Here, the curved surface area is
A=1000
mm
^2
the radius is
r=20
mm.
Thus,
A=2πrh\\ \Rightarrow 1000=2\times \frac { 22 }{ 7 } \times 20\times h\\ \Rightarrow 1000\times 7=2\times 22\times 20\times h\\ \Rightarrow 7000=880\times h\\ \Rightarrow h=\frac { 7000 }{ 880 } =7.96
Hence, height
of the cylinder is
7.96
m
m
.
The curved surface area of the cylinder is
2\pi r h
where as surface area of the cylinder is
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0%
\pi r(r+h)
0%
\pi rl(r+h)
0%
2\pi r(r+h)
0%
2\pi r^2l(r+h)
Explanation
The curved surface area of the cylinder is
2\pi r h
where as surface area of the cylinder is
2\pi 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.
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0%
\displaystyle 240\pi { cm }^{ 2 }
0%
\displaystyle 120\pi { m }^{ 2 }
0%
\displaystyle 220\pi { m }^{ 2 }
0%
\displaystyle 230\pi { mm }^{ 2 }
Explanation
Curved surface area of cylinder is
A=2πrh
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=2πrh=2\times π\times 6\times 10=120π
m
^2
Hence, the c
urved surface area
of the cylinder is
120π
m
^2
.
Choose the correct formula for surface area of a cylinder.
Report Question
0%
\displaystyle 2\pi { r }^{ 2 }+2\pi rh
0%
\displaystyle \pi { r }^{ 2 }+\pi rh
0%
\displaystyle 2\pi r+2\pi rh
0%
\displaystyle 2\pi { r }^{ 2 }+\pi rh
Explanation
A cylinder comprises two circles and one rectangle as given in the figure
The surface area of a circle is
\pi r^2
where
r
is the radius and the surface area of a rectangle is
2\pi rh
.
\implies
Surface area of cylinder
=2\times
area of the circular base
+
area of the rectangle
\Rightarrow
Surface area of cylinder
=2\pi r^2+2\pi rh
Find the area of the curved surface of a cylindrical box with radius 12 inches and height 20 inches.
Report Question
0%
\displaystyle 1505.1{ in }^{ 2 }
0%
\displaystyle 1506.5{ in }^{ 2 }
0%
\displaystyle 1507.5{ in }^{ 2 }
0%
\displaystyle 1507.2{ in }^{ 2 }
Explanation
Curved surface area of cylinder is
A=2πrh
Here, the radius is
12
in and height is
20
in.
Thus,
A=2πrh=2\times 3.14\times 12\times 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%
\displaystyle 0.46\pi
0%
\displaystyle 0.46\pi { m }^{ 3 }
0%
\displaystyle 0.46\pi { m }^{ 2 }
0%
\displaystyle 0.46\pi cm
Explanation
Given: Radius of cylinder
r=0.1m
and Height
h=2.2m
.
Surface area of a cylinder =
\displaystyle 2\pi r\left( r+h \right)
\displaystyle =2\times \pi \times 0.1\left( 0.1+2.2 \right)
\displaystyle =2\times \pi \times 0.1\left( 2.3 \right)
\displaystyle =0.46\pi { m }^{ 2 }
So, option C is correct.
Find the surface area of a cylinder:
r=9\ in, h=18\ in
Report Question
0%
\displaystyle 1526.04{\ in }^{ 2 }
0%
\displaystyle 1525.03{\ in }^{ 2 }
0%
\displaystyle 1526.04\ in
0%
\displaystyle 1526.04{\ in }^{ 3 }
Explanation
Surface area of cylinder is
A=2πr(r+h)
Here, radius is
r=9
in and the height is
h=18
in.
Thus,
A=2πr(r+h)=2\times 3.14\times 9(9+18)=56.52\times 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
\displaystyle \pi ={ 22 }/{ 7 }
)
Report Question
0%
\displaystyle 88{ ft }^{ 2 }
0%
\displaystyle 198{ ft }^{ 2 }
0%
\displaystyle 79{ ft }^{ 2 }
0%
\displaystyle 176{ ft }^{ 2 }
Explanation
Volume of a cylinder
=
\displaystyle \pi { r }^{ 2 }h
\Rightarrow \displaystyle 616=\frac { 22 }{ 7 } \times { r }^{ 2 }\times 4
\Rightarrow \displaystyle \frac { 616\times 7 }{ 22\times 4 } ={ r }^{ 2 }
\Rightarrow \displaystyle { r }^{ 2 }=49
\Rightarrow \displaystyle r=\sqrt { 49 } =7ft
Curved surface area
=
\displaystyle 2\pi rh
\displaystyle =2\times \frac { 22 }{ 7 } \times 7\times 4
\displaystyle =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
\displaystyle \pi ={ 22 }/{ 7 }
).
Report Question
0%
\displaystyle 880{ \ m }^{ 3 }
0%
\displaystyle 880{\ m }^{ 2 }
0%
\displaystyle 88{ \ m }^{ 2 }
0%
\displaystyle 880{\ mm }^{ 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
\therefore
Lateral Surface area
=2\pi(R-r)h
=2\times \dfrac{22}{7}\times (12-8)\times 35
=2\times 22\times 4 \times 5
=880 m^2
If the lateral surface of a cylinder is
\displaystyle 500\ { cm }^{ 2 }
and ts height is
10\ cm
, then find radius of its base. (use
\displaystyle \pi =3.14
).
Report Question
0%
6.92\ cm
0%
7.96\ cm
0%
\displaystyle 6.54\ cm
0%
\displaystyle 8.22\ cm
Explanation
Here, the lateral surface area is
A=500\ cm^2
and the height is
h=10\ cm
Let, the radius be
r
Lateral surface area of cylinder is
A=2πrh
Thus,
A=2πrh\\ \Rightarrow 500=2\times 3.14\times r\times 10\\ \Rightarrow 500=62.8r\\ \Rightarrow r=\dfrac { 500 }{ 62.8 } =7.96
Hence, radius
of the cylinder is
7.96\ cm
.
The circumference of a circle is
200
feet and height is
12
feet. Find its curved surface area of a cylinder.
Report Question
0%
\displaystyle 2400{ ft }^{ 2 }
0%
\displaystyle 2100{ ft }^{ 2 }
0%
\displaystyle 2300{ ft }^{ 2 }
0%
\displaystyle 2010{ ft }^{ 2 }
Explanation
Circumference of cylinder is
C=2πr
It is given that the circumference is
200
feet, therefore,
C=2πr\\ \Rightarrow 200=2πr\\ \Rightarrow r=\dfrac { 200 }{ 2π } =\dfrac { 100 }{ π }
Now, curved surface area of cylinder is
A=2πrh
Here, the radius is
\dfrac { 100 }{ π }
ft and height is
12
ft.
Thus,
A=2πrh=2π\times \dfrac { 100 }{ π } \times 12=2\times 100\times 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%
\displaystyle 23936{\ ft }^{ 3 }
0%
\displaystyle 23936{\ ft }^{ 2 }
0%
\displaystyle 23950{ \ ft }^{ 2 }
0%
\displaystyle 23936\ ft
Explanation
Surface area of cylinder is
A=2πr(r+h)
Here the cylindrical bin has radius
r=56
ft and height
h=12
ft.
Thus,
A=2πr(r+h)=2\times 3.14\times 56(56+12)=351.68\times 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%
\displaystyle 1507.2{ m }^{ 2 }
0%
\displaystyle 1527.6{ m }^{ 2 }
0%
\displaystyle 1517.8{ m }^{ 2 }
0%
\displaystyle 1588.1{ m }^{ 3 }
Explanation
Given,
Height
h=40\ m
Diameter =
\displaystyle 12m
Radius
r= \dfrac {Diameter}{2} = \dfrac {12}{2}\ m = 6
m
Curved surface area
=\displaystyle 2\pi rh
\displaystyle =2\times 3.14\times 6\times 40\ m^2
\displaystyle = 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
\displaystyle \pi =3.14
).
Report Question
0%
\displaystyle 4019.2{ cm }^{ 3 }
0%
\displaystyle 4019.2cm
0%
\displaystyle 4019.2{ cm }^{ 2 }
0%
\displaystyle 4018.6{ cm }^{ 2 }
Explanation
Surface area of cylinder is
A=2πr(r+h)
Here, radius is
r=20
cm and the height is
h=12
cm.
Thus,
A=2πr(r+h)=2\times 3.14\times 20(20+12)=125.6\times 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
\displaystyle 220{\ ft }^{ 2 }
. Round your answer to the nearest whole number.
(use
\displaystyle \pi ={ 22 }/{ 7 }
).
Report Question
0%
0.1
ft
0%
3
ft
0%
2
ft
0%
1
ft
Explanation
Surface area of cylinder is
A=2πr(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=2πr(r+h)\\ \Rightarrow 220=2\times \frac { 22 }{ 7 } \times 5(5+h)\\ \Rightarrow 220=\frac { 44 }{ 7 } (25+5h)\\ \Rightarrow 220\times 7=1100+220h\\ \Rightarrow 1540-1100=220h\\ \Rightarrow 220h=440\\ \Rightarrow h=\frac { 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
\displaystyle 200{ in }^{ 2 }
. Find surface area of cylindrical drum.(
\displaystyle \pi ={ 22 }/{ 7 }
)
Report Question
0%
\displaystyle 203.5{ in }^{ 2 }
0%
\displaystyle 207.3{ in }^{ 2 }
0%
\displaystyle 215.7{ in }^{ 2 }
0%
\displaystyle 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
\pi = 3.14
Report Question
0%
\displaystyle 5810.10in
0%
\displaystyle 5810.10{ in }^{ 2 }
0%
\displaystyle 5878.08{ in }^{ 2 }
0%
\displaystyle 5878{ in }^{ 2 }
Explanation
Surface area of cylinder is
A=2πr(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=2πr(r+h)=2\times 3.14\times 24(24+15)=150.72\times 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
\displaystyle 340\pi
. What is its height?
Report Question
0%
5 m
0%
6m
0%
7m
0%
8m
Explanation
Surface area of cylinder is
A=2πr(r+h)
Here the cylindrical container has surface area
A=340π
m
^2
and radius
r=10
m.
Thus,
A=2πr(r+h)\\ \Rightarrow 340π=2π\times 10(10+h)\\ \Rightarrow 340π=20π(10+h)\\ \Rightarrow 340π=200π+20πh\\ \Rightarrow 20πh=340π-200π\\ \Rightarrow 20πh=140π\\ \Rightarrow h=\dfrac { 140π }{ 20π } =7
Hence, the height
of the cylindrical container is
7m
.
Find the total surface area of the cylinder. (Use
\displaystyle \pi =3.14
).
Report Question
0%
\displaystyle 678.99{ ft }^{ 2 }
0%
\displaystyle 3881.05{ ft }^{ 2 }
0%
\displaystyle 3881.04ft
0%
\displaystyle 678.24{ ft }^{ 2 }
Explanation
Given:
r=6ft
and
h=12ft
The total surface area of a cylinder =
\displaystyle 2\pi r\left( r+h \right)
\displaystyle =2\times 3.14\times 6\left( 6+12 \right)
\displaystyle =2\times 3.14\times 6\left( 18 \right)
=\displaystyle 678.24{ ft }^{ 2 }
So, option D is correct.
The surface area of a cylindrical box is
\displaystyle 132\ { mm }^{ 2 }
and its height is
4 \ mm.
Find its radius.
Report Question
0%
\displaystyle 2
{ mm }
0%
\displaystyle 3
{ mm }
0%
\displaystyle 4
{ mm }
0%
\displaystyle 5
{ mm }
Explanation
Given: Cylindrical box has surface area
A=132
mm^2
and height
h=4\ mm
We know surface area of cylinder is
A=2πr(r+h)
Thus,
132=2\times \dfrac { 22 }{ 7 } \times r(r+4)
\Rightarrow 132=\dfrac { 44 }{ 7 } r(r+4)
\Rightarrow 132\times 7=44r(r+4)
\Rightarrow 924=44r^{ 2 }+176r
\Rightarrow 44r^{ 2 }+176r-924=0
\Rightarrow r^{ 2 }+4r-21=0
\Rightarrow r^{ 2 }+7r-3r-21=0
\Rightarrow r(r+7)-3(r+7)=0
\Rightarrow r+7=0,\quad r-3=0
\Rightarrow r=-7,\quad 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
\displaystyle 590{ in }^{ 2 }
. Find the height of the cylinder. (
\displaystyle \pi =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=2πr(r+h)
Here the wooden cylinder has surface area
A=590
in
^2
and radius
r=6
mm.
Thus,
A=2πr(r+h)\\ \Rightarrow 590=2\times \dfrac { 22 }{ 7 } \times 6(6+h)\\ \Rightarrow 590=\dfrac { 44 }{ 7 } (36+6h)\\ \Rightarrow 590\times 7=1584+264h\\ \Rightarrow 4130-1584=264h\\ \Rightarrow 264h=2546\\ \Rightarrow h=\dfrac { 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
cm^3
0%
452.16
cm^3
0%
252.16
cm^3
0%
152.16
cm^3
Explanation
Given, radius of hemisphere
=6
cm
Volume of the hemisphere
=
\dfrac{2}{3}\pi r^3
=
\dfrac{2}{3}\times 3.14 \times 6^3
= 452.16
cm^3
A gas cylinder has a diameter of
14
m and height is
0.2
m. Find its surface area. (
\displaystyle \pi ={ 22 }/{ 7 }
)
Report Question
0%
\displaystyle 316.512{ mm }^{ 2 }
0%
\displaystyle 316.512m
0%
\displaystyle 316.512{ m }^{ 3 }
0%
\displaystyle 316.512{ m }^{ 2 }
Explanation
Surface area of cylinder is
A=2πr(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=2πr(r+h)=2 \times \dfrac {22}{7}\times 7(7+0.2)=316.512
Hence, the surface area
of the gas cylinder is
316.512m^2
.
The curved surface area of a cylinder is
\displaystyle 188.4\ { m }^{ 2 }
. The height is
12\ m
. What is the radius? (use
\displaystyle \pi =3.14
).
Report Question
0%
\displaystyle 2\ { cm }
0%
\displaystyle 2.5\ cm
0%
\displaystyle 2\ m
0%
\displaystyle 2.5\ m
Explanation
Curved surface area of cylinder is
A=2πrh
Here, the curved surface area is
A=188.4\ m^2
the height is
h=12\ m
.
Thus,
A=2πrh\\ \Rightarrow 188.4=2\times 3.14\times r\times 12\\ \Rightarrow 188.4=75.36r\\ \Rightarrow r=\dfrac { 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\ mm
.
Report Question
0%
\displaystyle 195.33{ \ m }^{ 3 }
0%
\displaystyle 175.33{ \ mm }^{ 3 }
0%
\displaystyle 195.33{ \ mm }^{ 3 }
0%
\displaystyle 185.33{\ mm }^{ 3 }
Explanation
Formula:
Volume of sphere
=\dfrac{4}{3} \pi r^3
r=radius
Given:
diameter(d)=7.2\ mm
radius(r)=\dfrac{d}{2}=\dfrac{7.2}{2}=3.6\ mm
\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}\times 3.14\times (3.6)^3
=\dfrac{4}{3}\times 3.6\times 3.6\times 3.6\times 3.14
=\dfrac{4}{3}\times 46.656times 3.14
=\dfrac{585.999}{3}
=195.33\ mm^3
What is the volume of a sphere? (use
\displaystyle \pi =3.14
)
Report Question
0%
\displaystyle 6,878.82{\ in }^{ 3 }
0%
\displaystyle 6,578.82{ \ in }^{ 3 }
0%
\displaystyle 5,878.82{\ in }^{ 3 }
0%
\displaystyle 6,808.82{\ in }^{ 3 }
Explanation
Formula:
Volume of sphere
=\dfrac{4}{3}\pi r^3
where,
r=radius
Given:
r=11.8
After substituting the values in the formula we
\dfrac{4}{3}\pi r^3 =\dfrac{4}{3}\times 3.14\times 11.8^3
=\dfrac{4}{3}\times3.14\times11.8\times11.8\times11.8
=\dfrac{20636.481}{3}
=6878.82\ in^3
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