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

Answer:

The volume ratio of Prism A to Prism B is $\frac{729}{8}$

Step-by-step 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

$z^{2}=\frac{x}{y}$

we have

$\frac{x}{y}=\frac{81}{4}$

substitute

$z^{2}=\frac{81}{4}$

$z=\frac{9}{2}$

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

$z^{3}=\frac{x}{y}$

we have

$z=\frac{9}{2}$

substitute

$(\frac{9}{2})^{3}=\frac{x}{y}$

$(\frac{729}{8})=\frac{x}{y}$