 Important for :
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 4π 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 4π 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.