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3 years ago

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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.

1 answer:

Damm [24]3 years ago

8 0

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

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

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

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where the last fact is due to the law of total probability:

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By definition of conditional probability, we have

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We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

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By the law of total probability,

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$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

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