The radius and height of a cylinder are in the ratio 7 ∶ 13 and its volume is 6006 cm³. Its radius will be:

(Use π = \(\frac{22}{7}\))

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 25 Jun, 2024 Shift 1)

Answer 1

Given:

The radius and height of a cylinder are in the ratio 7:13, and its volume is 6006 cm³.

π = 22⁄7

Formula used:

Volume of a cylinder = πr²h

Calculation:

Let the radius be 7x and the height be 13x.

Volume = πr²h

⇒ 6006 = (22⁄7) × (7x)² × 13x

⇒ 6006 = (22⁄7) × 49x² × 13x

⇒ 6006 = (22 × 49 × 13)⁄7 × x³

⇒ 6006 = 2002x³

⇒ x³ = 6006 ÷ 2002 = 3

⇒ x = ∛3

Now, radius = 7x = 7 × ∛3 = 7 × 3\(\frac{1}{3}\) cm

∴ The correct answer is 7 × 3\(\frac{1}{3}\) cm.