The curved surface area of a right cylinder is 3696 cm2. Its height is

1.	The curved surface area of a right cylinder is 3696 cm2. Its height is three times its radius. What is the capacity (in litres) of the cylinder? (tame π =\(\frac{22}{7}\)1. 19.008 litres2. 30.87 litres3. 25.872 litres4. 29.75 litres
Answer» Correct Answer - Option 3 : 25.872 litres Given: The curved surface area of the right cylinder = 3696 cm² Height of cylinder = 3 × radius of the cylinder Formula used: The curved surface area of cylinder = 2πrh Volume of cylinder = πr²h Where, r = radius of cylinder h = height of cylinder Concept used: 1 cm³ = 0.001 litre Calculation: Let the radius of the cylinder be ‘r’ and the height of the cylinder be ‘h’. Curved surface area of cylinder = 2πrh ⇒ 2πrh = 3696 ⇒ 2πr × 3r = 3696 (h = 3r) ⇒ r² = (3696 × 7)/(22 × 6) ⇒ r² = 196 ⇒ r = 14 cm ⇒ h = 3r = 3 × 14 = 42 cm Volume of cylinder = πr²h ⇒ (22/7) × 14 × 14 × 42 ⇒ 25872 cm³ We know, 1 cm³ = 0.001 litre ⇒ 25872 × 0.001 ⇒ 25.872 litres ∴ The volume of the cylinder is 25.872 litres.

The curved surface area of a right cylinder is 3696 cm2. Its height is three times its radius. What is the capacity (in litres) of the cylinder? (tame π =\(\frac{22}{7}\)1. 19.008 litres2. 30.87 litres3. 25.872 litres4. 29.75 litres

Answer» Correct Answer - Option 3 : 25.872 litres

Given:

The curved surface area of the right cylinder = 3696 cm²

Height of cylinder = 3 × radius of the cylinder

Formula used:

The curved surface area of cylinder = 2πrh

Volume of cylinder = πr²h

Where,

r = radius of cylinder

h = height of cylinder

Concept used:

1 cm³ = 0.001 litre

Calculation:

Let the radius of the cylinder be ‘r’ and the height of the cylinder be ‘h’.

Curved surface area of cylinder = 2πrh

⇒ 2πrh = 3696

⇒ 2πr × 3r = 3696 (h = 3r)

⇒ r² = (3696 × 7)/(22 × 6)

⇒ r² = 196

⇒ r = 14 cm

⇒ h = 3r = 3 × 14 = 42 cm

Volume of cylinder = πr²h

⇒ (22/7) × 14 × 14 × 42

⇒ 25872 cm³

We know, 1 cm³ = 0.001 litre

⇒ 25872 × 0.001

⇒ 25.872 litres

∴ The volume of the cylinder is 25.872 litres.