Question

A spherical tank has a capacity of 750 gallons. Using the fact that one gallon is about $0.1337{\mathrm{ft}}^3$, find the radius of the tank.

Short answer

The radius of the tank is $27.01\mathrm{feet}$.

Step-by-step solution

Step-1. Volume of sphere.

The volume of the sphere is $V=\frac{4}{3}\pi r^3$, where r is the radius.

Step-2. Setup the model.

Capacity of the sphere is$750\mathrm{gallons}.$

Volume of one gallon is$0.1337{\text{ft}}^{\text{3}}$

We need to find the radius of the sphere.

Thus, the volume of spherical tank is:

$750\times 0.1337{\text{ft}}^3=100.275{\text{ft}}^3$

Step-3. Solve for radius.

Substitute the respective values into the volume formula.

$\begin{array}{l}\frac{4}{3}\pi r^3=100.275\\ r^3=\frac{3\left(100.275\right)}{4\pi }\\ r=\sqrt[3]{\frac{300.825}{4\times 3.14}}\\ r\approx 27.01\end{array}$

Hence, the radius of the tank is $27.01\text{feet}$.