Question

The standard formula for the volume of a cone is V=πr2h3. If the cone 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=πr2h3to V' = V × k3 for a scaled cone.

Answer 1

The volume of a cone with base radius r and height h is

$V = \frac 1 3 \pi r^2 h$

What happens when we scale by k ?

Let V' be the volume of a cone with radius rk and height hk

$V' = \frac 1 3 \pi (rk)^2 (hk) = \frac 1 3 \pi r^2 k^2 h k = k^3 (\frac 1 3 \pi r^2 h) = k^3 V$

Answer 2

Answer: V= pi*r^2

Step-by-step explanation

V’=[pi(r*k)^2(h*k)]/3

=[pi*k^2r^2*kh]/3

=k^3 *[pi*r^2*h]/3

=k^3 *V^3