Question

4. The volume of a sphere is 524 in'. Another sphere has a radius that is 3 times larger.

What is the volume of the larger sphere?

Answer 1

Answer:

V_larger ≈ 14,137 in^3

Explanation:

The formula for the volume of a sphere is

V = (4/3)πr^3,

where "r" is the radius of the sphere and π (pi) is a mathematical constant approximately equal to 3.14159.

Let's first calculate the radius of the smaller sphere using its volume:

V = (4/3)πr^3
524 = (4/3)πr^3
r^3 = (524 * 3/4π)
r ≈ 5.10 inches

Now, let's calculate the radius of the larger sphere, which is 3 times larger than the radius of the smaller sphere:

r_larger = 3r
r_larger ≈ 3 * 5.10
r_larger ≈ 15.3 inches

Finally, we can calculate the volume of the larger sphere using its radius:

V_larger = (4/3)πr_larger^3
V_larger = (4/3)π(15.3)^3
V_larger ≈ 14,137 in^3

Therefore, the volume of the larger sphere is approximately 14,137 cubic inches.