If the radius of a sphere increases from 3 feet to 9 feet, by how many cubic feet does the volume of the sphere increase? A 96πft3 B 108πft3 C 936πft3 D 972πft3

Correct answer: C. 936π ft³

Step-by-step explanation:

The formula for the volume of a sphere is:

V = 4/3 r³ π

Let the radius of the first sphere be r₁ = 3 ft and the second r₂ = 9 ft

Increasing the volume of the sphere is equals to the difference of V₂ and V₁

ΔV = V₂ - V₁ = 4/3 r₂³ π - 4/3 r₁³ π = 4/3 π (r₂³ - r₁³) = 4/3 π (9³ - 3³)

ΔV = 4/3 π (729 - 27) = 4/3 π · 702 = 4 · 234 · π = 936 π ft³

ΔV = 936 π ft³

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