Question

The circumference of the base of a cone is 132 cm and its volume is 3234 cm³.Find the height 
1. 6 cm
2. 7 cm
3. 8 cm
4. 9 cm

Answer 1

Correct Answer - Option 2 : 7 cm

Given

Circumference of the base of rod = 132 cm

Volume of rod = 3234 cm³

 Formula used

Circumference of circle = 2πr

Volume of cone = (1/3)πr²h

Calculation

2πr = 132

⇒ 2 × (22/7) × r = 132

⇒ r = (132 × 7)/(2 × 22)

⇒ r = 21 cm

(1/3)πr²h = 3234

⇒ (1/3) × (22/7) × 21 × 21 × h = 3234

⇒ h = (3234 × 7 × 3)/(22 × 21 × 21)

⇒ h = 7 cm

∴ Height of cone is 7 cm