Question

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28cm. Find the C. S. A OF THE Cone?

Answer 1

$\large \tt AHOY!! \:$

given :-

volume of the cone = 9856cm³

diameter of the cone = 28cm

therefore it's radius = 28/2

= 14cm

volume of the cone = 1/3πr²h

=> 1/3πr²h = 9856cm³

=> 1/3 × 22/7 × 14 × 14 × h = 9856cm³

=> 22/3 × 2 × 14 × h = 9856cm³

=> 616/3 × h = 9856cm³

=> h = 9856/1 × 3/616

=> h = 29558/616

=> h = 48cm

formula for the CSA of a cone is πrl. where 'l' is the slant height of the cone.

ATQ, it's a right circular cone. so we can easily find the slant height of the cone by Pythagoras theorem considering slant height as hypotenuse, radius as base and height as perpendicular.

we know that h² = b² + p²

=> h² = 14² + 48²

=> h² = 196 + 2304

=> h² = 2500

=> h = √2500

=> h = 50cm

hence the slant height of the cone is 50cm.

CSA of the cone = πrl

= 22/7 × 14 × 50

= 22 × 2 × 50

= 2200cm²

$\large \tt HOPE \: THIS \: HELPS!!$