The standard formula for the volume of a cylinder is V = πr2h. If the cylinder is scaled proportionally by a factor of k, its volume becomes V' = V * k3. Use your algebra skills to derive the steps that lead from V = πr2h to V' = V * k3 for a scaled cylinder. Show your work.

Question

Derick Bennett

25 February, 00:00

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Answers (1)

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Jeffrey Montes · Answer 1

So, r' (the new r) becomes kr, and h'=h*k,

so V' = pi * (r') ^2*h' = pi * (r*k) ^2 * (h*k) = pi*r^2*h*k^3 = V * k^3

Convinced?