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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 $16$ feet and a height of $8$ feet. Container B has a diameter of $8$ 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 the empty space inside Container A, to the nearest tenth of a cubic foot?

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Weighted averages: word problems

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Q. Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of

16

feet and a height of

8

feet. Container B has a diameter of

8

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 the empty space inside Container A, to the nearest tenth of a cubic foot?

Calculate Volume Container A: Calculate the volume of Container A using the formula for the volume of a cylinder, $V = \pi r^2 h$ , where $r$ is the radius and $h$ is the height. The radius of Container A is half the diameter, so $r = \frac{16 \text{ feet}}{2} = 8 \text{ feet}$ . The height $h = 8 \text{ feet}$ . $V = \pi(8 \text{ feet})^2(8 \text{ feet})$ .
Calculate Volume Container B: Perform the calculation for the volume of Container A: $V = \pi(64)(8) = \pi(512)$ cubic feet.
Subtract Volumes: Calculate the volume of Container B using the same formula, $V = \pi r^2 h$ . The radius of Container B is half the diameter, so $r = \frac{8 \text{ feet}}{2} = 4 \text{ feet}$ . The height $h = 18 \text{ feet}$ . $V = \pi(4 \text{ feet})^2(18 \text{ feet})$ .
Perform Subtraction: Perform the calculation for the volume of Container B: $V = \pi(16)(18) = \pi(288)$ cubic feet.
Calculate Empty Space Volume: Subtract the volume of Container B from the volume of Container A to find the empty space in Container A. Volume of Container A - Volume of Container B = $\pi(512)$ cubic feet - $\pi(288)$ cubic feet.
Use Approximation: Perform the subtraction: $\pi(512) - \pi(288) = \pi(224)$ cubic feet. This is the volume of the empty space in Container A.
Use Approximation: Perform the subtraction: $\pi(512) - \pi(288) = \pi(224)$ cubic feet. This is the volume of the empty space in Container A.Use the value of $\pi$ as approximately $3.14$ to calculate the volume of the empty space in Container A to the nearest tenth: $3.14 \times 224 \approx 703.36$ cubic feet.

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