MATH SOLVE

4 months ago

Q:
# A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 . What is the volume of the dilated prism? Enter your answer, as a decimal, in the box.

Accepted Solution

A:

First, you must find the original volume of the prism by applying the following formula:

V1=HxB

V1 is the original volume of the prism.

H is the height of the prism (H=10 ft).

B is the base are of the prism (B=5 ft2)

So, the original volume is:

V1=HxB

V1=(10 ft)(5 ft2)

V1=50 ft2

When the prism is dilated by a factor of 6/5, its volume is:

V2=(V1)*(6/5)^3

V2=(50 ft³)*(6/5)^3

V2= 86.4 ft³

What is the volume of the dilated prism?

The answer is: 86.4 ft³

V1=HxB

V1 is the original volume of the prism.

H is the height of the prism (H=10 ft).

B is the base are of the prism (B=5 ft2)

So, the original volume is:

V1=HxB

V1=(10 ft)(5 ft2)

V1=50 ft2

When the prism is dilated by a factor of 6/5, its volume is:

V2=(V1)*(6/5)^3

V2=(50 ft³)*(6/5)^3

V2= 86.4 ft³

What is the volume of the dilated prism?

The answer is: 86.4 ft³