Question

The ratio of the surface areas of two spheres is 3:2. If the volume of the larger sphere is 2,916 in³, what is the volume of the smaller sphere?

A) 1,587 in³

B) 5,357 in³

C) 864 in³

Answer 1

The volume of the smaller sphere can be found by determining the ratio of their volumes based on the given ratio of their surface areas.

Step-by-step explanation:

To find the volume of the smaller sphere, we need to determine the ratio of their volumes based on the given ratio of their surface areas. Since the ratio of the surface areas of the spheres is 3:2, this means the ratio of their volumes will be the cube root of that, which is approximately 1.144.

Let's denote the volume of the smaller sphere as V. We can set up the equation:

V / 2916 = 1.144³

Multiplying both sides by 2916:

V = 2916 * 1.144³

Using a calculator, we find that V is approximately 1586.758 cubic inches. Therefore, the volume of the smaller sphere is approximately 1587 cubic inches. So, the correct answer is A) 1,587 in³