Question

A sphere of radius 14 cm is melted to form a cone of radius 7 cm and height h, if the total no. of cones formed is 32, then, what is the value of h (in m)?
1. 0.14 m
2. 0.07 m
3. 0.7 m
4. 1.4 m

Answer 1

Correct Answer - Option 2 : 0.07 m

Given:

Radius of sphere = 14 cm

Radius of cone = 7 cm

Height of cone = h

Number of cones formed = 32

Formula Used:

Volume of sphere = 4/3 × πR³

Volume of cone = 1/3 × πr²h

Calculation:

Volume of sphere = 4/3 × πR³

⇒ 4/3 × π × 14³
Volume of cone = 1/3 × πr²h

⇒ 1/3 × π × 7² × h

According to question –

⇒ 4/3 × π × 14³ = 32 × 1/3 × π × 7² × h

⇒ (4 × 14³) = 32 × 7² × h

⇒ h = 7 cm

⇒ h = 0.07 m

∴ The height of the cone (h) is 0.07 m.