Question

The area of the base of a conical solid is 38.5 cm² and its volume is 154 cm³. Find the curved surface area of the solid.

Answer 1

Area of the base, πr² = 38.5 cm² 

Volume of the solid, V = 154 cm³ 

Curved surface area of the solid = πr²h 

Volume, V `= 1/3 pir^2h` 

`=> 154 = 1/3 pir^2h` 

`=> h = (154 xx 3)/(pir^2)` 

`=> h = (154 xx 3)/38.5`

= 12 cm

Area = 38.5

πr² = 38.5 

`=> r^2 = 38.5/3.14` 

`=> r = sqrt(38.5/3.14)`

= 3.5 

Curved surface area of solid = πrl

= `pirsqrt(r^2 + h^2)` 

= `22/7 xx 3.5 xx sqrt(3.5^2 + 12^2)` 

= `22/7 xx 3.5 xx 12.5` 

= 137.5 cm²