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# question

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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 28 feet and a height of 15 feet. Container B has a diameter of 22 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full. To the nearest tenth, what is the percent of Container A that is empty after the pumping is complete?

May 7, 2020

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cylinder A has a volume of $$\left(\frac{d}{2}\right)^2\pi h = 14^2\pi \cdot 15 = 2940\pi$$ and cylinder B has a volume of $$\left(\frac{d}{2}\right)^2\pi h = 11^2\pi \cdot 159= 2299\pi$$. this means that cylinder B is $$\frac{2299}{2940} \cdot 100 \approx 0.7819 \cdot 100 \approx 78.2\%$$ percent of cylinder A, which means cylinder A will end up being

$$100-78.2=\boxed{21.8\%}$$

percent full after the pumping.

May 7, 2020