Question

1The volumes of two similar prisms are 972 cm3 and 36 cm3. The surface area of the larger prism is 594 cm2.

What is the scale factor for the similar figures? What is the surface area of the smaller prism?

Answer 1

Part 1)

The scale factor of the smaller prism to the larger prism is 3

or

The scale factor of the larger prism to the smaller prism is 1/3

Part 2) The surface area of the smaller prism is 66 square centimeters

Explanation:

Part 1) What is the scale factor for the similar figures?

we know that

If two figures are similar, then the ratio of their volumes is equal to the scale factor raised to the cube

Let

z ----> the scale factor

x ---> volume of the larger prism

y ---> volume of the smaller prism

so

`z^3=(x)/(y)`

we have

`x=972\ cm^3\\y=36\ cm^3`

substitute

`z^3=(972)/(36)`

Simplify

`z^3=27\\z=3`

therefore

The scale factor of the smaller prism to the larger prism is 3

or

The scale factor of the larger prism to the smaller prism is 1/3

Part 2) What is the surface area of the smaller prism?

we know that

If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared

Let

z ----> the scale factor

x ---> surface area of the larger prism

y ---> surface area of the smaller prism

so

`z^2=(x)/(y)`

we have

`x=594\ cm^2`

`z=3`

substitute

`3^2=(594)/(y)`

solve for y

`y=(594)/(9)=66\ cm^2`

therefore

The surface area of the smaller prism is 66 square centimeters