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» all » V n S Area Quiz 8
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V n S Area Quiz 8
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V n S Area Quiz 2
V n S Area Quiz 1
Direction: Study the following questions carefully and choose the right answer.
important for :
CDSE
CGL Tier 2
CGLTier 1
SSC 10+2
1.
What is the quantity of cloth required to roll up to form a right circular tent whose base is of radius 12 m and height 5 cm ?
A.
40π sq m
B.
60π sq m
C.
78π sq m
D.
156π sq m
Ans
D
Explain it
Answer:
Option
D
Explanation:
Given that, radius of circular cone (r) = 12 m
Height of circular cone (h) = 5 m
∴ Required quantity of cloth to all upto form a right circular tent = Curved surface area of cone
= πrl
= πr
h
^{2}
+ r
^{2}
(∵ l =
h
^{2}
+ r
^{2}
)
= π × 12 ×
5
^{2}
+ 12
^{2}
= π × 12 ×
169
= π × 12 × 13 = 156π m
^{2}
= π × 12 ×
169
= π × 12 × 13 = 156π m
^{2}
Hence, option D is correct.
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2.
The volume of a hollow cube is 216x
^{3}
. What surface area of the largest sphere which be enclosed in it ?
A.
18πx
^{2}
B.
27πx
^{2}
C.
36πx
^{2}
D.
72πx
^{2}
Ans
C
Explain it
Answer:
Option
C
Explanation:
Given that,
Volume of cube = 216x
^{3}
⇒ (side)
^{3}
= (6x)
^{3}
⇒ side = 6x
∴ Diameter of sphere = Side of cube = 6x
and, radius of sphere (r) = 3x
Now, surface area of sphere = 4πr = 4π × (3x)
^{2}
= 36πx
^{2}
Hence, option C is correct.
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3.
What is the diameter of the largest circle lying on the surface of a sphere of surface area 616 sq cm ?
A.
14 cm
B.
10.5 cm
C.
7 cm
D.
3.5 cm
Ans
A
Explain it
Answer:
Option
A
Explanation:
Given that,
Surface area of sphere = 616 cm
^{2}
∴ 4πr
^{2}
= 616
⇒ r
^{2}
=
616
=
616 × 7
= 49
4π
4 × 22
⇒ r = 7 cm
∴ Diameter of largest circle lying on sphere = 2r = 2 × 7 = 14 cm
Hence, option A is correct.
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4.
What is the diameter of the largest circle lying on the surface of a sphere of surface area 616 sq cm ?
A.
14 cm
B.
10.5 cm
C.
7 cm
D.
3.5 cm
Ans
A
Explain it
Answer:
Option
A
Explanation:
Given that,
Surface area of sphere = 616 cm
^{2}
∴ 4πr
^{2}
= 616
⇒ r
^{2}
=
616
=
616 × 7
= 49
4π
4 × 22
⇒ r = 7 cm
∴ Diameter of largest circle lying on sphere = 2r = 2 × 7 = 14 cm
Hence, option A is correct.
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5.
If 64 identical small spheres are made out of big sphere of diameter 8 cm, then what is surface area of each small sphere ?
A.
π cm
^{2}
B.
2π cm
^{2}
C.
4π cm
^{2}
D.
8π cm
^{2}
Ans
C
Explain it
Answer:
Option
C
Explanation:
Given that, diameter of big sphere = 8 cm
∴ radius of big sphere (R) = 4 cm
Let radius of each small sphere = r
We know that,
Volume of each small sphere =
Volume of big sphere
Number of small sphere
⇒
4
πr
^{3}
3
=
4
πR
^{3}
3
64
⇒ r
^{3}
=
(4)
^{3}
= 1
64
⇒ r = 1 cm
Now, surface area of each small sphere = 4πr
^{2}
= 4π(1)
^{2}
= 4π cm
^{2}
Hence, option C is correct.
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