Question

The standard formula for the volume of a rectangular pyramid is . If the pyramid 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 to V' = V × k3 for a scaled rectangular pyramid. Show your work.

Answer 1

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The volume of a rectangular pyramid is equal to

$V=\frac{1}{3}LWH$

where

L is the length of the rectangular base

W is the width of the rectangular base

H is the height of the pyramid

If the pyramid is scaled proportionally by a factor of k

then

the new dimensions are

L=kL

W=kW

H=kH

substitute and find the new Volume V'

$V'=\frac{1}{3}(kL)(kW)(kH)$

$V'=\frac{1}{3}(k^{3})LWH$

$V'=(k^{3})\frac{1}{3}LWH$

$V'=(k^{3})V$

The new volume is equal to the scale factor k elevated to the cube multiplied by the original volume

Answer 2

Answer:

V = πr2h

V' = π × (k × r)2 × (k × h)

   = π × k2 r2 × kh

   = k3 × πr2h

   = k3 × V

Step-by-step explanation: