Question

The total surface area of a right circular cone with slant height 25 cm is 704cm², find the volume of the cone....

PLEASE HELP ME !!!​

Answer 1

1232 cm³

Explanation:

For a cone, the total surface area is

A = πrL + πr²

where L = slant height, r = radius

704 cm² = (25 cm)πr + πr²

πr² + 78.539816r - 704 = 0

Use the quadratic formula to solve for r.

`r = (-b + \pm√(b^2 - 4ac))/(2a)`

`r = (-78.539816 + \pm√((78.539816)^2 - 4(π)(-704)))/(2π)`

r = 7.00 or r = -32.00

We discard the negative value for the radius, and we keep r = 7.

Now we find the volume of a cone with r = 7 cm, L = 25

First, we find the height.

a² + b² = c²

(7)² + b² = (25)²

b = 24

height = 24 cm

V = (1/3)πr²h

V = (1/3)(π)(7 cm)²(24 cm)

V = 1232 cm³