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

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Answer 1 · 2015-07-04T15:32:41

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

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)