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Ghella [55]
2 years ago
11

If all the dimensions of the rectangular pyramid are multiplied by 1/5, what is the effect on the volume

Mathematics
1 answer:
Pachacha [2.7K]2 years ago
4 0

Answer:

If all the dimensions of the rectangular pyramid are multiplied by 1/5, the volume will be 125 times smaller.

Step-by-step explanation:

A rectangular pyramid has the following dimensions:

length(l), height(h) and width(w)

The volume is:

V = \frac{l*h*w}{3}

If all the dimensions of the rectangular pyramid are multiplied by 1/5

Then we have that:

l = \frac{l}{5}, w = \frac{w}{5}, h = \frac{h}{5}

The modified volume will be:

V_{M} = \frac{\frac{l}{5}*\frac{w}{5}*\frac{h}{5}}{3} = \frac{\frac{l*w*h}{125}}{3} = \frac{l*h*w}{125*3} = \frac{1}{125}(\frac{l*h*w}{3}) = \frac{V}{125}

So

If all the dimensions of the rectangular pyramid are multiplied by 1/5, the volume will be 1/125 of the original, that is, 125 times smaller.

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