P and Q are two geometrically similar solid shapes.

The total surface area of shape P is 720 cm².

The total surface area of shape Q is 2880 cm².

The volume of shape P is 3200 cmº.

Calculate the volume of shape Q.

25600cm³

Step-by-step explanation:

We are given these values from the question

The total surface area of shape P is 720 cm².

The total surface area of shape Q is 2880 cm².

The volume of shape P is 3200 cm³

Step 1

Find the scale factor of P to Q in terms of Length, Area and volume

Using the surface area value:

a. Scale factor for length

2880 cm² : 720 cm²

Divide through by 180

= 16 : 4 = 16/4

b. Scale factor for area

√ 16/4=> 4/2

c. Scale factor for volume

(4/2) ³

= 64/8

In order to determine the Volume of shape Q, we would multiply the scale factor of the volume by the volume of P

Volume of P = 3200 cm³

Volume of Q =

3200 cm³ * (64/8)

= 25600cm³