Question

PLEASE HELP ME!!!

P and Q are two geometrically similar solid shapes

The total surface area of shape P is 720cm^2.

The total surface area of shape Q is 2880cm^2


The volume of shape P is 3200cm^3


Calculate the volume of shape Q.

Answer 1

The volume of shape Q is
`25,600\ cm^(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 shape Q

y----> surface area of shape P

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

we have

`x=2,880\ cm^(2)`

`y=720\ cm^(2)`

substitute

`z^(2)=(2,880)/(720)`

`z=2`

step 2

Find the volume of shape Q

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 shape Q

y----> volume of shape P

`z^(3)=(x)/(y)`

we have

`z=2`

`y=3,200\ cm^(3)`

substitute

`2^(3)=(x)/(3,200)`

`x=(8)(3,200)=25,600\ cm^(3)`