Question

question
a tank in the shape of a hemisphere has a diameter of 10 feet. if the liquid that fills the tank has
a density of 58.2 pounds per cubic foot, what is the total weight of the liquid in the tank, to the
nearest full pound?

Explanation:

Step1: Find the radius of the hemisphere

The diameter \(d = 10\) feet. The radius \(r=\frac{d}{2}\), so \(r = 5\) feet.

Step2: Calculate the volume of the hemisphere

The volume formula for a hemisphere is \(V=\frac{2}{3}\pi r^{3}\). Substitute \(r = 5\) into the formula: \(V=\frac{2}{3}\pi(5)^{3}=\frac{2}{3}\pi\times125=\frac{250\pi}{3}\approx261.8\) cubic feet.

Step3: Calculate the weight of the liquid

The density \(
ho=58.2\) pounds per cubic foot. Use the formula \(m=
ho V\). Substitute \(
ho = 58.2\) and \(V\approx261.8\): \(m = 58.2\times261.8=58.2\times(260 + 1.8)=58.2\times260+58.2\times1.8=(60 - 1.8)\times260+(100 - 41.8)\times1.8=(60\times260-1.8\times260)+(100\times1.8-41.8\times1.8)=(15600 - 468)+(180 - 75.24)=15132+104.76 = 15236.76\approx15237\) pounds.

Answer:

15237