Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 3 feet and a height of 9 feet. Container B has a radius of 4 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.

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

47.1 cubic

Explanation:

Answer 2

The volume of the empty portion of Container B, to the nearest tenth of a cubic foot, is approximately 47.1 cubic feet.

Explanation:

The volume of water in Container A is given by the formula for the volume of a cylinder, which is:

V_A = πr^2h

where r is the radius and h is the height of the cylinder.

Substituting the values for Container A, we get:

V_A = π(3^2)(9) = 81π

The volume of Container B can also be calculated using the same formula:

V_B = πr^2h

Substituting the values for Container B, we get:

V_B = π(4^2)(6) = 96π

Since all the water in Container A is pumped into Container B, the total volume of water in Container B after the pumping is:

V_A = V_B = 81π

Now, to find the volume of the empty portion of Container B, we need to subtract the volume of the water from the total volume of Container B:

V_empty = V_B - V_A = 96π - 81π = 15π

Approximating π to 3.14, we get:

V_empty ≈ 15(3.14) = 47.1 cubic feet

Therefore, the volume of the empty portion of Container B, to the nearest tenth of a cubic foot, is approximately 47.1 cubic feet.