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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 7 feet and a height of 15 feet. Container B has a radius of 5 feet and a height of 17 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 the empty space inside Container A, to the nearest tenth of a cubic foot?

Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 7 feet and a height of 15 feet. Container B has a radius of 5 feet and a height of 17 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 the empty space inside Container A, to the nearest tenth of a cubic foot?

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Solution

To solve this problem, we first need to calculate the volume of both containers. The volume V of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height.

  1. Calculate the volume of Container A: V_A = π * (7ft)² * 15ft = 2310 cubic feet (rounded to the nearest whole number)

  2. Calculate the volume of Container B: V_B = π * (5ft)² * 17ft = 1335 cubic feet (rounded to the nearest whole number)

  3. Subtract the volume of Container B from the volume of Container A to find the volume of the empty space in Container A after the water is pumped into Container B: V_empty = V_A - V_B = 2310 cubic feet - 1335 cubic feet = 975 cubic feet

So, the volume of the empty space inside Container A after the water is pumped into Container B is approximately 975 cubic feet.

This problem has been solved

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