Question

two containers designed to hold water are side by side, both in the shape of a cylinder. container A has a diameter of 32 feet and a height of 16 feet. container B has a diameter of 30 feet and a height of 18 feet. container A is full of water and the water is pumped into container B until container B is completely full.After the pumping is complete, what is the volume of water remaining in container A to the nearest tenth of a cubic foot?

Answer 1

Given the word problem, we can deduce the following information:

Container A:

d=32 ft

h=16 ft

Container B:

d=30 ft

h=18 ft

To determine the volume of water remaining in container A, we first get the volume of container A by using the formula:

$V=\pi(\frac{d}{2})^2h$

We plug in what we know:

$\begin{gathered} V=\pi(\frac{d}{2})^{2}h \\ V=\pi(\frac{32}{2})^2(16) \\ Calculate \\ V=12867.96\text{ }ft^3 \end{gathered}$

Next, we get the volume of container B using the same formula:

$\begin{gathered} V=\pi(\frac{d}{2})^{2}h \\ V=\pi(\frac{30}{2})^2(18) \\ Calculate \\ V=12723.45\text{ }ft^3 \end{gathered}$

Now, we get the difference:

$\begin{gathered} Volume\text{ }Remaining=12867.96\text{ }ft^3-12723.45\text{ }ft^3 \\ Simplify \\ Volume\text{ }Remaining=144.5\text{ }ft^3 \end{gathered}$

Therefore, the answer is:

$\begin{equation*} 144.5\text{ }ft^3 \end{equation*}$