Question

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 original volume.

C.The volume will be 1/4 times the volume.

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

Answer 1

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

Answer 2

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.