Respuesta :

keeping in mind that, the diameter of A is 24, thus its radius is 12, and B's diameter is 22, thus its radius is 11.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\qquad \qquad \qquad \qquad \begin{array}{llll} \stackrel{\textit{volume of cylinder A}}{\pi(12^2)(18) }\implies 2592\pi \\\\\\ \stackrel{\textit{volume of cylinder B}}{\pi(11^2)(20) }\implies 2420\pi \end{array}[/tex]

how much is left?  well 2592π - 2420π, that much.
Container A is completely full while container B has nothing in it.

When container B is completely full after the pumping, the volume of water left in container A will be equivalent to the volume of container A subtracted by the volume of container B.

The volume of any right cylinder is [tex] \pi r^2 h[/tex] where r is the radius and h is the height of the cylinder.

The diameters of the cylinders are given. The radius is half of the diameters.
The radius of container A is 24/2, or 12. The radius of container B is 22/2, or 11.

[tex]\text{Volume of Container A}= \pi r^2 h = \pi \times 12^2 \times 18[/tex]
[tex]\approx 8138.88[/tex]

[tex]\text{Volume of Container B}= \pi r^2 h = \pi \times 11^2 \times 20[/tex]
[tex]\approx 7598.8[/tex]

Now, subtract the two volumes.

[tex]\text{Volume of Container A} - \text{Volume of Container B} = 540.08[/tex]

Rounding this to the nearest tenth of a cubic foot will give 540.1 cubic feet. Thus, container A will have approximately 540.1 cubic feet of water after container B is completely full.

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