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

Answer:

The volume of shape Q is $25,600\ cm^{3}$

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----> the scale factor

x----> surface area of shape Q

y----> surface area of shape P

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

we have

$x=2,880\ cm^{2}$

$y=720\ cm^{2}$

substitute

$z^{2}=\frac{2,880}{720}$

$z=2$

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

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

we have

$z=2$

$y=3,200\ cm^{3}$

substitute

$2^{3}=\frac{x}{3,200}$

$x=(8)(3,200)=25,600\ cm^{3}$