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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?

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 class=

Sagot :

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:

[tex]V=\pi(\frac{d}{2})^2h[/tex]

We plug in what we know:

[tex]\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}[/tex]

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

[tex]\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}[/tex]

Now, we get the difference:

[tex]\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}[/tex]

Therefore, the answer is:

[tex]\begin{equation*} 144.5\text{ }ft^3 \end{equation*}[/tex]

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