Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 14 feet and a height of 18 feet. Container B has a diameter of 18 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.

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

1501.7 ft

DELATAMATH

Explanation:

Answer 2

First, let's calculate the volume of water that was transferred from Container A to Container B.

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

For Container A:

radius = diameter/2 = 14/2 = 7 feet

height = 18 feet

V_A = π(7)^2(18) ≈ 2,443.96 cubic feet

For Container B:

radius = diameter/2 = 18/2 = 9 feet

height = 15 feet

V_B = π(9)^2(15) ≈ 3,817.01 cubic feet

So the volume of water transferred from Container A to Container B is:

V_water = V_A ≈ 2,443.96 cubic feet

After the transfer, Container B contains both the water that was originally in Container B and the water transferred from Container A. The total volume of water in Container B is:

V_total = V_B + V_water ≈ 6,261.97 cubic feet

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_water ≈ 3,817.01 - 2,443.96 ≈ 1,373.05 cubic feet

So the volume of the empty portion of Container B is approximately 1,373.05 cubic feet.