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Direction: Study the following questions carefully and choose the right answer.
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 ?
» Explain it
D
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 h2 + r2           (∵ l =  h2 + r2 )

= π × 12 ×  52 + 122  = π × 12 ×  169  = π × 12 × 13 = 156π m2

= π × 12 ×  169  = π × 12 × 13 = 156π m2

Hence, option D is correct.

2
The volume of a hollow cube is 216x3. What surface area of the largest sphere which be enclosed in it ?
» Explain it
C
Given that,

Volume of cube = 216x3

⇒  (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 = 36πx2

Hence, option C is correct.

3
What is the diameter of the largest circle lying on the surface of a sphere of surface area 616 sq cm ?
» Explain it
A
Given that,

Surface area of sphere = 616 cm2

∴  4πr2 = 616

⇒  r2 =  616  =  616 × 7  = 49
4 × 22

⇒  r = 7 cm

∴  Diameter of largest circle lying on sphere = 2r = 2 × 7 = 14 cm

Hence, option A is correct.
4
What is the diameter of the largest circle lying on the surface of a sphere of surface area 616 sq cm ?
» Explain it
A
Given that,

Surface area of sphere = 616 cm2

∴  4πr2 = 616

⇒  r2 =  616  =  616 × 7  = 49
4 × 22

⇒  r = 7 cm

∴  Diameter of largest circle lying on sphere = 2r = 2 × 7 = 14 cm

Hence, option A is correct.

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 ?
» Explain it
C
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 πr3
3
 = 
4 πR3
3
64
 

⇒  r3 =  (4)3  = 1
64

⇒  r = 1 cm

Now, surface area of each small sphere = 4πr2 = 4π(1)2 = 4π cm2

Hence, option C is correct.