Question

A metal sphere of radius 10.5 is melted and cast into right circular cones of radius equal to one-third of the radius of the sphere, each of height is 3 cm. The number of cones will be:
1. 126
2. 63
3. 105
4. 84

Answer 1

Correct Answer - Option 1 : 126

Given:

Radius of metallic sphere (R) = 10.5 cm

Radius of circular base of smaller cone (r) = 3.5 cm

Hight of cone (h) = 3 cm

Formula used:

The volume of a sphere = (4/3)πR3,

The volume of cone = (1/3) × πr2h

here, r = radius and h = height

Calculation:

According to the question,

Volume of metallic sphere (V) = (4/3)πR3

⇒ V = 4/3 × 22/7 × (10.5)³

The volume of cone = (1/3) × πr2h

⇒ V = 1/3 × 22/7 × (3.5)² × 3

Number of cones formed (n) = Volume of Sphere/Volume of Cone

⇒ n = [4/3 × 22/7 × (10.5)3]/[1/3 × 22/7 × (3.5)2 × 3]

⇒ n = 4851/38.5 = 126​

∴ The number of cones will be 126.