PLZ HELP! DUE IN 10 MINUTES!! I just need the second box! I believe the first one is correct also...

PLZ HELP! DUE IN 10 MINUTES!! I just need the second box! I believe the first one is correct also..

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Ответ:

gharrell03

10.05.2022

Mathematics

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

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

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

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

we have

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

substitute

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

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

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