Question

The diameter of the base of the cone is 24x cm.
The height of the cone is 16x cm.

The curved surface area of the cone is 2160pi cm^2.
The volume of the cone is V pi cm^3, where V is an integer.

What is the value of V. Answer is cm^2.

Thanks a lot.

Answer 1

πr√(r^2+h^2) = 2160π
(12x)√(144x^2+256x^2) = 2160
(12x)(20x) = 2160
x^2 = 9
x = 3

so, the volume is

π/3 r^2h
= (π/3) (24*3)^2 (16*3)
= 82944π

V = 82944 cm^3

Answer 2

Steve's answer is incorrect.

In the final stage, he said (24*3)^2.
However, 24 is not the RADIUS of the cone's base. It is the DIAMETER.

Therefore, you must halve 24.
The final calculation should hence be:
V = (π/3) (12*3)^2 (16*3)
= 20736