Question

5. Two similar figures have volumes 27 in.? and 125 in.?. The surface area of the smaller figure is 63 in.. (1 point)

Answer 1

Answer:

$175\ in^{2}$

Step-by-step explanation:

step 1

Find the scale factor

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 of the larger solid

y----> volume of the smaller solid

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

we have

$x=125\ in^{3}$

$y=27\ in^{3}$

substitute

$z^{3}=\frac{125}{27}$

$z=\frac{5}{3}$

step 2

Find the surface area of the larger solid

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 of the larger solid

y----> surface area of the smaller solid

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

we have

$z=\frac{5}{3}$

$y=63\ in^{2}$

substitute

$(\frac{5}{3})^{2}=\frac{x}{63}$

$x=\frac{25}{9}*63=175\ in^{2}$