Question

The circumference of the base of a right circular cone is 44 7 cm and its slant height
is 28 cm. Find the volume of the cone.

Answer 1

EXPLANATION.

Circumference of the base of the cone is 44√7 cm.

It's slant height is 28 cm.

As we know that,

Formula of :

Circumference of the base = 2πr.

Slant height (l) : l² = r² + h².

Using this formula in this question, we get.

⇒ 2πr = 44√7.

⇒ 2 x 22/7 x r = 44√7.

⇒ 44/7 x r = 44√7.

⇒ r/7 = √7.

⇒ r = 7√7 cm.

Radius of cone is 7√7 cm.

⇒ l² = r² + h².

⇒ (28)² = (7√7)² + h².

⇒ 784 = 343 + h².

⇒ h² = 441.

⇒ h = 21 cm.

Height of cone is 21 cm.

To find : The volume of cone.

Volume of cone = 1/3πr²h.

⇒ 1/3 x 22/7 x (7√7)² x 21.

⇒ 1/3 x 22/7 x 343 x 21.

⇒ (22 x 343 x 21)/(21).

⇒ 22 x 343 = 7546 cm³.

∴ Volume of cone is 7546 cm³.