Question

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 19 feet. Container B has a diameter of 20 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.

To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?

Answer 1

18.9% is the answer

Explanation:

volume of a cylinder = πd²/4 x h

where d is diameter and h is height of cylinder.

thus

vol of A is

`vol \: of \: a \: = \pi * \frac{ {d}^(2) }{4} * h \\ = \pi * \frac{ {16}^(2) }{4} * 19 \\ = \pi * 4 * 16 * 19 \\ = 3818.24`

and

`vol \: of \: b = \pi * \frac{ {20}^(2) }{4} * 15 \\ = \pi * 5 * 20 * 15 \\ = 4710`

difference in vol of a and b is

`diff \: = vol \: of \: b \: - vol \: of \: a \\ = 4710 - 3818.24 \\ = 891.76`

this volume will remain empty after container A is pumped into container B.

this volume as a percentage of total volume of B is

`\% = (diff \: vol)/(total \: vol) * 100 \\ = (891.76)/(4710) * 100 \\ = 18.9\%`