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

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`

`\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.