Question

The height of a right circular cone is 12cm. If it's volume is 100π cm^3,find its slant height

Answer 1

Given:-

• Height of a right circular cone,h = 12 cm

• Volume of circular cone , V = 100π cm³

To find out:-

Find the slant height ( l ) .

Solution:-

We know that,

Volume of cone = 1/3 × π × r² × h

⇒ 100π = 1/3 × π × r² × 12

⇒ 100π = 12/3 π × r²

⇒ 100π = 4π × r²

⇒ r² = 100π/4π

⇒ r² = 25

⇒ r = √25

⇒ r = 5 cm

Now,

By using Pythagoras therome:

l² = r² + h²

⇒ l² = ( 5 )² + ( 12 )²

⇒ l² = 25 + 144

⇒ l² = 169

⇒ l = √169

⇒ l = 13 cm

Hence,the slant height of a right circular cone is 13 cm.