Question

Find the surface area of a cone with volume 320pi and height 15 (hint: don't use the height in

the surface area formula.

Answer key :
Either 200 pi or 325 pi
Please help !!!

Answer 1

200π

Explanation:

Surface area of a cone = πr(r+l)

r is the radius

l is the slant height

Volume of the cone = 1/3πr²h

320π = 1/3πr²h

320 = 1/3r²(15)

320 = 5r²

r² = 320/5

r² = 64

r = 8

l² = 15² + 8²

l² = 225 + 64

l² = 289

l = 17

Get the surface area;

S = πr(r+l)

S = π8(8+17)

S = π*8*25

S = 200π

Hence the surface area of the cone is 200π