Question

Prism A is similar to Prism B. The ratio of the surface area of Prism A to Prism B is 81:4. Find the volume ratio of Prism A to Prism B.

Answer 1

The volume ratio of Prism A to Prism B is
`(729)/(8)`

Explanation:

Step 1

Find the scale factor

we know that

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

Let

z-----> scale factor

x/y----> ratio of the surface area of Prism A to Prism B

so

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

we have

`(x)/(y)=(81)/(4)`

substitute

`z^(2)=(81)/(4)`

`z=(9)/(2)`

step 3

Find the volume ratio of Prism A to Prism B.

we know that

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

Let

z-----> scale factor

x/y----> volume ratio of Prism A to Prism B

so

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

we have

`z=(9)/(2)`

substitute

`((9)/(2))^(3)=(x)/(y)`

`((729)/(8))=(x)/(y)`