Question

A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm has lateral surface area equal to

Answer 1

Height of frustum ( H ) = 16 cm.



Radius of top of the frustum ( R ) = 20 cm.


And,


Radius of bottom of the frustum ( r ) = 8 cm.



Slant Height ( L ) = √(H)² + ( R - r )²



=> ✓ ( 16)² + ( 20 - 8 )²



=> ✓ 256 + (12)²



=> √256 + 144



=> √400


=> 20 cm.


Therefore,



Lateral Surface Area of the frustum of a cone = πL ( R + r ) cm².




=> 22/7 × 20 ( 20 + 8 ) cm².




=> ( 22 × 20 ) / 7 × 28 cm².



=> ( 22 × 20 × 4 ) cm².



=> 1760 cm².

Answer 2

Height of frustum ( H ) = 16 cm.



Radius of top of the frustum ( R ) = 20 cm.


And,


Radius of bottom of the frustum ( r ) = 8 cm.



Slant Height ( L ) = √(H)² + ( R - r )²



=> ✓ ( 16)² + ( 20 - 8 )²



=> ✓ 256 + (12)²

√256 + 144

20



Lateral Surface Area of the frustum = πL ( R + r ) cm².

22/7 × 20 ( 20 + 8 ) cm².

22 × 20 ) / 7 × 28 cm².

22 × 20 × 4 ) cm².
1760 cm².