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Question Video: Finding the Height of a Cylinder Whose Volume Is Equal to the Volume of Another Cylinder Mathematics • 8th Grade

The two given cylinders have the same volume. Determine β„Ž to the nearest tenth.

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Video Transcript

The two given cylinders have the same volume. Determine β„Ž to the nearest tenth.

In the figure, we are shown two cylinders together with their radii and heights. We are told that they have the same volume and are asked to calculate the height β„Ž of the second cylinder.

We recall that the volume of a cylinder can be calculated using the formula 𝑉 is equal to πœ‹π‘Ÿ squared β„Ž. The first cylinder has a radius of 16 centimeters and a height of 12 centimeters. So, its volume is equal to πœ‹ multiplied by 16 squared multiplied by 12. The second cylinder has a radius of 15 centimeters and a height β„Ž. So, its volume is equal to πœ‹ multiplied by 15 squared multiplied by β„Ž.

Since the cylinders have the same volume, we know that these two expressions are equal. We can solve for β„Ž by firstly dividing through by πœ‹. Next, we divide through by 15 squared so that β„Ž is equal to 16 squared multiplied by 12 divided by 15 squared. This is equal to 1024 over 75, which as a decimal is 13.653 and so on. Since we are asked to give our answer to the nearest tenth, the height β„Ž is equal to 13.7 centimeters.

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