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.

The answer in the procedure

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

so

 and

The volume of the original cylinder is equal to

If the cylinder is scaled proportionally by a factor of k

then

the new radius is ------>

the new height is ------>

The volume of the scaled cylinder is equal to

substitute the values

Remember that

so

substitute

The volume of the scaled cylinder is equal to the scale factor elevated to the cube multiplied by the volume of the original cylinder

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step-by-step explanation:

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