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 74.4 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?

Answer 1

Step 1

State the volume of a hemisphere.

`v=(2)/(3)\pi r^3`

Where;

`\begin{gathered} r=(diameter)/(2)=(10)/(2)=5ft \\ \end{gathered}`

Step 2

Find the volume of the hemisphere

`v=(2)/(3)*\pi*5^3=(250\pi)/(3)ft^3`

Step 3

Find the total weight of the liquid in the tank

`\begin{gathered} \text{Density}=\frac{mass}{\text{volume}} \\ 74.4=(mass)/((250\pi)/(3)) \\ \text{mass}=19477.87445lb \\ \text{mass}\approx19478lb \end{gathered}`

Hence the total weight of the liquid in the tank to the nearest full pound = 19478lb