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Mashutka [201]
3 years ago
9

How will the volume of the pyramid change if each side is multiplied by a factor of 1/2?

Mathematics
2 answers:
slamgirl [31]3 years ago
4 0
D,The volume will be 1/8 times the volume.
kakasveta [241]3 years ago
4 0

Answer:

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

Step-by-step 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

\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*\frac{1}{2}=\frac{x}{2},

y*\frac{1}{2}=\frac{y}{2},  

z*\frac{1}{2}=\frac{z}{2}

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

\text{Volume of new pyramid}=\frac{x}{2}*\frac{y}{2}*\frac{z}{2}

\text{Volume of new pyramid}=\frac{x*y*z}{2*2*2}

\text{Volume of new pyramid}=\frac{x*y*z}{8}

\text{Volume of new pyramid}=\frac{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.

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