Question

Three solid shapes A, B and C are similar.

Answer 1

Answer:

$\frac{3}{10}$

Step-by-step explanation:

step 1

Find the ratio of the height of shape A to the height of shape B

we know that

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

Let

z-----> the scale factor

x----> surface area shape A

y----> surface area shape B

so

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

substitute

$z^{2} =\frac{4}{25}$

$z =\frac{2}{5}$

therefore

the ratio of the height of shape A to the height of shape B is equal to

$\frac{hA}{hB}=\frac{2}{5}$

step 2

Find the ratio of the height of shape B to the height of shape C

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-----> the scale factor

x----> volume shape B

y----> volume shape C

so

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

substitute

$z^{3} =\frac{27}{64}$

$z =\frac{3}{4}$

therefore

the ratio of the height of shape B to the height of shape C is equal to

$\frac{hB}{hC}=\frac{3}{4}$

step 3

Find the ratio of the height of shape A to the height of shape C

we have

$\frac{hA}{hB}=\frac{2}{5}$

$\frac{hB}{hC}=\frac{3}{4}$

Multiply

$(\frac{hA}{hB})(\frac{hB}{hC})=\frac{hA}{hC}$

so

$(\frac{2}{5})(\frac{3}{4})=\frac{6}{20}=\frac{3}{10}$