How do I find the surface area of a sphere that has a volume of 288 cubic inches?

1 Answer
Jul 4, 2015

Answer:

The surface area is #"210.90 in"^2#.

Explanation:

Here is one way to solve the problem.

The formula for the volume of a sphere is

#V = 4/3πr^3#

We can solve this for #r#.

#3V = 4πr^3# or #4πr^3 = 3V#

#r^3 = (3V)/(4π)#

#r^3 = ("3× 288 in"^3)/(4π) = 216/π "in"^3 = "68.7549 in"^3#

#r = root3("68.7549 in"^3 ) = "4.0967 in"#

Now we can insert this value of #r# into the formula for the area of a sphere.

#A = 4πr^2 = 4π × ("4.0967 in")^2 = 4π×"16.2879 in"^2 = "210.90 in"^2# (to two decimal places)