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Problem 21 Hard Difficulty

Find the volume of the empty space in a cylindrical tube of three tennis balls. The diameter of each ball is about 2.5 inches. The cylinder is 2.5 inches in diameter and is 7.5 inches tall.

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Video Transcript

so we have a cylinder that contains three tennis balls. We know that the cylinder has a diameter of 2.5 inches and a height of 7.5 inches, and each tennis ball has a diameter of 2.5 inches. Were asked to find the volume of the empty space within the cylinder. To do this, we need to find the volume of the cylinder and subtract from it the volume of all three tennis balls, so three times the volume of each ball. The formula for the volume of a cylinder is pi r squared H and the formula for the volume of a ball. Remember, we're multiplying it by three would be 4/3. Pi are cute. Now all we need to do is substitute the values for our variables. We don't yet know what the radius is, but we do know that the diameter is equal to twice the radius. The diameter of the cylinder is the same as the diameter of each tennis ball, so the radius will be the same for both as well. 2.5 is equal to two are divide both sides by two, and we have a radius of 1.25 inches. Now we can substitute that value. PI times the radius of 1.25 squared times the height of 7.5 minus three times 4/3 pi times of radius of 1.25 Cute and I highly recommend using a calculator for this. So let's go ahead and pop over to Dismas, where we have pi times 1.25 squared times 7.5 So that's the volume of our cylinder, and we want to subtract from that three times the volume of each tennis ball. So three times 4/3 hi times, a radius of 1.25 Cute. And we have approximately 12.27 If we round that to the nearest 10th our volume is approximately 12.3 cubic inches.