The external and the internal radii of a hollow right circular

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The external and the internal radii of a hollow right circular cylinder of height 15 cm. are 6.75 cm. and 5.25 cm. respectively. If it is melted to form a solid cylinder of height half of the original cylinder, then the radius of the solid cylinder is

1. 6 cm.
2. 6.5 cm.
3. 7 cm.
4. 7.25 cm.

Correct Option: A

Volume of the metal of hollow cylinder = π(R² – r²) h
= π (6.752 – 5.252) × 15
= π (6.75 + 5.25) (6.75 – 5.25) × 15
= π × 12 × 1.5 × 15 cu. cm.
If the radius of the base of solid cylinder be r₁ cm, then
πr₁² h₁ = π × 12 × 1.5 × 15

⇒ r₁² ×	15	= 12 × 1.5 × 15
	2

= 12 × 1.5 × 2
⇒ r₁² = 36
⇒ r₁ = 36 = 6 cm.