Question

question a tank in the shape of a hemisphere has a diameter of 8 feet. if the liquid that fills the tank has a density of 86 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 \(d = 8\) feet. The radius \(r=\frac{d}{2}\), so \(r = 4\) feet.

Step2: Calculate the volume of the hemisphere

The volume formula for a hemisphere is \(V=\frac{2}{3}\pi r^{3}\). Substitute \(r = 4\) into the formula:

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Step3: Calculate the weight of the liquid

We know that density \(
ho=86\) pounds per cubic foot. Weight \(W=
ho\times V\). Substitute \(V = \frac{128\pi}{3}\) and \(
ho = 86\):

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Answer:

\(11522\) pounds