How will the volume of the pyramid change if each side is multiplied by a factor of 1/2? A.The volume will be 2 times the original volume. B.The volume will be 8 times the origi…

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asked Jul 28, 2017 190k views

2 Answers

Veles · Answer 1 · 2017-08-02T08:32:35+0000

Answer:

D. The volume will be 1/8 times the volume.

Explanation:

We have been asked to find the affect on the volume of a pyramid if each side is multiplied by factor of 1/2.

Let x and y be the sides of base of pyramid and z be the height of original pyramid.

$\text{Volume of pyramid}=\text{Base area*Height}$

$\text{Volume of pyramid}=x*y*z$

Now each side of our pyramid is multiplied by a factor of 1/2, so sides of new pyramid will be:

x*(1)/(2)=(x)/(2) ,

y*(1)/(2)=(y)/(2) ,

z*(1)/(2)=(z)/(2)

Let us substitute sides of new pyramid in volume formula to figure out volume of new pyramid.

$\text{Volume of new pyramid}=(x)/(2)*(y)/(2)*(z)/(2)$

$\text{Volume of new pyramid}=(x*y*z)/(2*2*2)$

$\text{Volume of new pyramid}=(x*y*z)/(8)$

$\text{Volume of new pyramid}=(1)/(8)*(x*y*z)$

We can see that volume of new pyramid is 1/8 times the volume of original pyramid, therefore, option D is the correct choice.