Question

Here are two similar solid shapes.

and
A
surface area of shape A: surface area of shape B = 3:4
The volume of shape B is 10 cm³
Work out the volume of shape A.
Give your answer correct to 3 significant figures.
B

Answer 1

Explanation:

Let the volume of shape A be V. Since the surface area of shape A is 3/4 times that of shape B, the surface area of shape A is 3/7 times the total surface area of the two shapes combined.

Therefore, the surface area of shape A is:

3/7 (surface area of shape A + surface area of shape B) = 3/7 (4/3 surface area of shape B) = 12/21 surface area of shape B

We know that the volume of shape B is 10 cm³, and we can find the volume of shape A by using the ratio of the volumes to the ratio of the surface areas:

V/10 = 3/4

V = 7.5 cm³ (to 3 significant figures)

Therefore, the volume of shape A is 7.5 cm³.