Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 32 feet and a height of 16 feet. Container B has a diameter of 30 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full. After the pumping is complete, what is the volume of water remaining in Container A, to the nearest tenth of a cubic foot?

Answer 1

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

For Container A, the radius is half the diameter, or 16 feet. So the volume of Container A is:

V_A = π(16 ft)^2(16 ft) = 8,192π cubic feet

For Container B, the radius is half the diameter, or 15 feet. So the volume of Container B is:

V_B = π(15 ft)^2(18 ft) = 12,735π cubic feet

To find the volume of water that was transferred from Container A to Container B, we can subtract the volume of Container A from the volume of both containers combined:

V_water = V_A + V_B - V_A = V_B

V_water = 12,735π cubic feet

To find the volume of water remaining in Container A, we can subtract the volume of water that was transferred from the volume of Container A:

V_remaining = V_A - V_water

V_remaining = 8,192π - 12,735π

V_remaining ≈ -3,543.7 cubic feet

However, a negative volume doesn't make sense in this context, so we know that there must be no water remaining in Container A after the transfer. Therefore, the volume of water remaining in Container A to the nearest tenth of a cubic foot is 0.