Question

The surface area of two similar solids is 121 yards squared and 361 yards squared. The volume of the larger solid is 1747 yards cubed. What is the volume of the smaller solid?

Answer 1

The volume of the smaller solid is
`339\ yd^(3)`

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----> the scale factor

x----> surface area of the larger solid

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

`z^(2)=(x)/(y)`

we have

`x=361\ yd^(2)`

`y=121\ yd^(2)`

substitute

`z^(2)=(361)/(121)`

`z=(19)/(11)`

step 2

Find the volume of the smaller solid

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)=(x)/(y)`

we have

`z=(19)/(11)`

`x=1,747\ yd^(3)`

substitute

`((19)/(11))^(3)=(1,747)/(y)\\ \\((6,859)/(1,331))=(1,747)/(y) \\ \\y=1,331*1,747/6,859\\ \\y=339\ yd^(3)`