Question

{curved surface area of cone=550cm square}
height=24
find volume of this cone ??
********please explain me ******

Answer 1

Let the radius be r and slant height be l

According to question,

CSA = 550

=> pi × r × l = 550

=> 22 r × l / 7 = 550

=> r × l = 550 × 7 / 22

=> r × l = 25 × 7

=> r [ sqrt ( r^2 + h^2 ) ] = 175

On squaring both sides, we get

r^2 ( r^2 + 24^2) = 175 × 175

=> r^4 + 576r^2 - 30625 = 0

=> r^4 + 625r^2 - 49 r^2 - 30625 = 0

=> r^2 ( r^2 + 625 ) - 49 ( r^2 + 625 ) = 0

=> ( r^2 + 625) ( r^2 - 49 ) = 0

Now,

If r^2 + 625 = 0 , then the radius will be imaginary number which is not possible .

If r^2 - 49 = 0

=> r^2 = 49

=> r = 7

Now,

Volume = pi r^2 h / 3

= 22 × 7 × 7 × 24 / 3 × 7

= 22 × 7 × 8

= 154 × 8

= 1232 cm^3