Question

An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top.

Answer 1

6 inches

Explanation:

correct on Plato/ edmentum courseware

Answer 2

The volume of a sphere:

`V=(4)/(3) \pi r^3`
r - the radius

3392.92 cubic inches are poured into 30 spheres.

`3392.92=30 * (4)/(3) \pi r^3 \\ \\ 3392.92=40\pi r^3 \ \ \ \ \ \ \ \ \ \ \ \ |/ 40 \\ \\ 84.823=\pi r^3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ \pi \\ \\ r^3=(84.823)/(\pi) \\ \\ r=\sqrt[3]{(84.823)/(\pi)} \\ \\ r \approx \sqrt[3]{27} \\ \\ r \approx 3`

The diameter is twice the radius.
The diameter of each sphere should be approximately 6 inches.