Question

Two containers designed to hold water are side by side, both in the shape of a

cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 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?
Container A
play
Container B
10
d12
8
h6
O

Answer 1

Answer: 7.4%

Note: you may not need to type in the percent sign.

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Step-by-step explanation:

Let's find the volume of water in container A.

Use the cylinder volume formula to get

V = pi*r^2*h

V = pi*5^2*8

V = 200pi

The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.

We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.

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Now find the volume of cylinder B

V = pi*r^2*h

V = pi*6^2*6

V = 216pi

Despite being shorter, tank B can hold more water (since it's more wider).

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Now divide the results of each section

(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%

This shows us that 92.59% of tank B is 200pi cubic feet of water.

In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.

This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%

Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.

Answer 2

Answer: Volume of Cylinder A is pi times the area of the base times the height

π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3

Volume of Cylinder B is likewise pi times the area of the base times the height

π r2 h = (3.1416)(6)(6)(7) = 791.68 ft3

After pumping all of Cyl A into Cyl B

there will remain empty space in B 791.68 – 753.98 = 37.7 ft3

The percentage this empty space is

of the entire volume is 37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth

.

Step-by-step explanation: I hope that help you.