Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 10 feet and a height of 12 feet. Container B has a diameter of 14 feet and a height of 9 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 water in Container B, 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 diameter of 10 feet and a height of 12 feet. Container B has a diameter of 14 feet and a height of 9 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 water in Container B, to the nearest tenth of a cubic foot?
Solution
To solve this problem, we first need to calculate the volume of water in Container A, which is full. The volume V of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height.
Step 1: Calculate the volume of water in Container A The radius of Container A is half of its diameter, so r = 10 feet / 2 = 5 feet. The height h is 12 feet. So, the volume of water in Container A is V = π * (5 feet)² * 12 feet = 300π cubic feet.
Step 2: Pump the water from Container A to Container B When the water from Container A is pumped into Container B, the volume of the water doesn't change. So, the volume of water in Container B is also 300π cubic feet.
Step 3: Convert the volume to the nearest tenth of a cubic foot To convert the volume to the nearest tenth of a cubic foot, we can use the approximate value of π, which is 3.14. So, the volume of water in Container B is approximately 300 * 3.14 = 942 cubic feet.
So, after the pumping is complete, the volume of water in Container B is approximately 942 cubic feet.
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