Question

a tank in the shape of a hemisphere has a radius of 4 feet. if the liquid that fills the tank has a density of 75 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?

Explanation:

Step1: Calculate the volume of the hemisphere

The volume formula for a hemisphere is \(V=\frac{2}{3}\pi r^{3}\). Given \(r = 4\) feet, we substitute into the formula:
\(V=\frac{2}{3}\pi(4)^{3}=\frac{2}{3}\pi\times64=\frac{128\pi}{3}\) cubic feet.

Step2: Calculate the weight of the liquid

We know that weight \(W=\text{density}\times\text{volume}\). The density \(
ho = 75\) pounds per cubic foot.
\(W = 75\times\frac{128\pi}{3}\)
First, \(75\div3=25\), then \(W=25\times128\pi\)
\(W = 3200\pi\)
Using \(\pi\approx3.14159\), \(W\approx3200\times3.14159 = 10053.088\)

Answer:

\(10053\)