7776π in³
Step-by-step explanation:
You are given the area of the sphere, so you can use the area formula to find its radius. Then the volume formula can be used to find the volume.
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radius
The area of the sphere is given by the formula ...
A = 4πr²
Solving for r, we find ...
A/(4π) = r²
√(A/(4π)) = r = √(1296π/(4π)) = √324 = 18
The radius of the sphere is 18 inches.
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volume
The volume formula is ...
V = 4/3πr³
Using the found radius, we find the volume to be ...
V = 4/3π(18 in)³ = 4/3(5832)π in³
V = 7776π in³