Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 22 feet and a height of 19 feet. Container B has a diameter of 28 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.

After the pumping is complete, what is the volume of the empty portion of Container B, to the nearest tenth of a cubic foot?

Answer 1

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder.

For Container A, the radius is half the diameter, so r = 22/2 = 11 feet. The height is 19 feet. Therefore, the volume of Container A is:

V(A) = π(11^2)(19) ≈ 7,958.8 cubic feet

All of the water from Container A is pumped into Container B, so the volume of water in Container B is also 7,958.8 cubic feet.

For Container B, the radius is half the diameter, so r = 28/2 = 14 feet. The height is 18 feet. Therefore, the volume of Container B is:

V(B) = π(14^2)(18) ≈ 10,937.4 cubic feet

After the water is pumped from Container A to Container B, the volume of water in Container B is 7,958.8 cubic feet. Therefore, the volume of the empty portion of Container B is:

V(empty portion of B) = V(B) - 7,958.8 ≈ 2,978.6 cubic feet

Rounding to the nearest tenth of a cubic foot, the volume of the empty portion of Container B is approximately 2,978.6 cubic feet.

Answer 2

`\textsf{Volume of the empty portion of Container B} =\tt \bold{\underline{3861\textsf{ cubic feet}}}`

Explanation:

First, we need to find the radius of each container.

`\textsf{The radius of Container A}\tt (R_A)=( 22)/(2) = 11\textsf{ feet}`

`\textsf{The radius of Container B}\tt (R_B)=( 28)/(2) = 14\textsf{ feet}`

`\textsf{The height of Container A}\tt (H_A )= 19 \textsf{ feet}`

`\textsf{The height of Container B}\tt (H_B )= 18 \textsf{ feet}`

We can then use the formula for the volume of a cylinder to find the volume of each container.

`\boxed{\textsf{The volume of a cylinder }=\boxed{ \pi * r^2 * h.}}`

The volume of Container A =
`\tt \pi * 11^2 * 19 = 7222.52 \textsf{ cubic feet.}`

The volume of Container B =
`\tt \pi * 14^2 * 18 = 11083.54 \textsf{ cubic feet.}`

Since the water from Container A is pumped into Container B, the volume of the empty portion of Container B is the difference between the volumes of the two containers.

The volume of the empty portion of Container B :

`\tt 11083.54\textsf{ cubic feet} - 7222.52\textsf{ cubic feet} = 3861.02\textsf{ cubic feet}`

To the nearest tenth of a cubic foot, the volume of the empty portion of Container B is
`\tt 3861\textsf{ cubic feet}`

So the answer is
`\tt \bold{\underline{3861\textsf{ cubic feet}}}`