Question

What is the least number of full spherical containers needed to completely fill up the fish tank?

Answer 1

The least number of the spherical container is 1,909

To get the least number, what we have to do is to find the volume of both

So, we have to divide the volume of the tank by the volume of the sphere

The volume of the tank is the product of the length, width and height of the tank

We have this as;

$100\times100\times100\text{ = 1,000,000 cubic in}$

To get the volume of the container, we use the formula for the volume of the container with the radius 5 in as follows;

$\begin{gathered} V\text{ = }\frac{4}{3}\times\pi\times r^3 \\ \\ V\text{ = }\frac{4}{3}\times\frac{22}{7}\times5^3=^{}523.6\text{ cubic inches} \end{gathered}$

Dividing the volumes to get the least number, we have;

$\frac{1,000,000}{523.6}\text{ = 1,909.85}$

This means the least number of the spherical container that will fill the fish tank is 1,909