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:The answer in the procedureStep-by-step explanation:we know thatThe volume of a rectangular pyramid is equal to [tex]V=\frac{1}{3}LWH[/tex]whereL is the length of the rectangular baseW is the width of the rectangular baseH is the height of the pyramidIf the pyramid is scaled proportionally by a factor of kthen the new dimensions areL=kLW=kWH=kHsubstitute and find the new Volume V'[tex]V'=\frac{1}{3}(kL)(kW)(kH)[/tex][tex]V'=\frac{1}{3}(k^{3})LWH[/tex][tex]V'=(k^{3})\frac{1}{3}LWH[/tex][tex]V'=(k^{3})V[/tex]The new volume is equal to the scale factor k elevated to the cube multiplied by the original volume