If the slant height of a cone is 18.7 cm and the curved surface area is 602.8 cm², find the volume of cone. (π = 3.14)

Given.

Slant height of cone = 18.7 cm

CSA of cone = 602.8 cm²

Formula used/Theory.

Volume of cone = πr²h

CSA of cone = πrl

In cone,

CSA of cone = 602.8 cm²

πrl = 602.8 cm²

3.14 × r × 18.7cm = 602.8 cm²

r = = 10.26 cm

In cone,

The Radius, height and slant height makes a right angled triangle

With hypotenuse as slant height of triangle

∴ By Pythagoras Theorem

Radius² + Height² = (slant height) ²

Height² + (10.26 cm) ² = (18.7 cm) ²

Height² + 105.26 cm² = 349.69 cm²

Height² = 349.69 cm² – 105.26 cm²

Height = √(244.43 cm²) = 15.63 cm

Volume of Cone = πr²h

= × 3.14 × 10.26cm × 10.26cm × 15.63cm

= 3.14 × 10.26cm × 10.26cm × 5.21cm

= 1722.11 cm³