The standard formula for the volume of a rectangular pyramid is . If the pyramid is scaled proportionally by a factor of k, its volume becom

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.

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Luna 8 mins 2021-09-15T18:36:06+00:00 2 Answers 0

Answers ( )

    0
    2021-09-15T18:37:24+00:00

    Answer:

    V = πr2h

    V’ = π × (k × r)2 × (k × h)

       = π × k2 r2 × kh

       = k3 × πr2h

       = k3 × V

    Step-by-step explanation:

    0
    2021-09-15T18:37:54+00:00

    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

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