Question

A hollow metallic sphere has internal and external radius of 3 cm and 5 cm respectively. It is melted and recast as a solid cylinder with radius 7 cm. What is the height of the cylinder?
1. 3 cm
2. 8 cm
3. \(\frac{8}{3}\) cm
4. \(\frac{2}{3}\) cm

Answer 1

Correct Answer - Option 3 : \(\frac{8}{3}\) cm

Given:

The internal radius of hollow sphere = 3 cm

The external radius of hollow sphere = 5 cm

Radius of cylinder = 7 cm

Formula used:

Volume of hollow sphere = 4/3π × (R³ – r³)

Volume of cylinder = πr²h

Calculation:

According to the question

Volume of hollow sphere = 4/3 × π × (5³ – 3³)

⇒ 4/3 × π × (125 – 27)

⇒ 4/3 × π × 98

⇒ 392π/3 cm³

Now,

Volume of cylinder = volume of the sphere

⇒ πr²h = 392π/3

⇒ π × (7)² × h = 392π/3

⇒ 49π × h = 392π/3

⇒ h = (392π/49π × 3)

⇒ h = 8/3 cm

∴ The height of the cylinder is 8/3 cm