# 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

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