Question

Find the surface area of a sphere that has a volume of 288 cu. in.

what i am doing is multiplying 288 by 4/3 to get back to the origional radius squared
i get 384
sence that is alredy the radius squared i just plug it into the sphere area formula
(4 pi radius squared) and multiply it by 4
and i get 1536 pi
i know that is incorrect because my answer choices are
48 pi
144 pi
20,736pi
what am i doing wrong?

Answer 1

The key idea is that both the surface area and the volume are related to the radius

Answer 2

so solve for the radius and then find the surface area

Answer 3

Volume = (4/3)pi r^3 = 288

Answer 4

r^3 = 216/pi

Answer 5

r = cuberoot(216/pi) = cuberoot(216)/cuberoot(pi) = 6/cuberoot(pi)

Answer 6

Surface area = 4 pi r^2 = 4pi(6/cuberoot(pi))^2 = 144pi/cuberoot(pi^2)
= 144cuberoot(pi)

Answer 7

Answer=144cuberoot(pi)

Answer 8

Have you got it ?

Answer 9

so next time i should solve 4 the radius and not just plug it in

Answer 10

ok thanks a million!!:)