Question Video: Calculating the Density of a Cylinder Mathematics

A cylinder has a radius of 9 feet and a height of 20 feet. It has a mass of 1,100 pounds. Work out, to two decimal places if needed, the density of the cylinder, knowing that density = mass/volume.

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Video Transcript

A cylinder has a radius of nine feet and a height of 20 feet. It has a mass of 1,100 pounds. Work out, to two decimal places if needed, the density of the cylinder, knowing that density is equal to mass divided by volume.

We can use this formula to calculate the density. We know that the mass is 1,100 pounds. However, we don’t know the volume of the cylinder. The volume of any cylinder is equal to πœ‹π‘Ÿ squared β„Ž. We are told that the cylinder has a radius of nine feet and a height of 20 feet. We can, therefore, substitute π‘Ÿ equals nine and β„Ž equals 20 into this formula. The volume 𝑉 is equal to πœ‹ multiplied by nine squared multiplied by 20. Nine squared is equal to 81. Multiplying this by 20 gives us 1,620. Therefore, 𝑉 is equal to the 1,620πœ‹. The volume of the cylinder is, therefore, equal to 1,620πœ‹ cubic feet.

Volume is always measured in cubic units. And as the radius and height were in feet, the volume will be in cubic feet. We can now calculate the density of the cylinder by dividing the mass by the volume. We need to divide 1,100 by 1,620πœ‹. Typing this into the calculator gives us an answer of 0.2161 and so on. We are asked to give this answer to two decimal places. This means that 𝐷 is equal to 0.22.

The density of the cylinder is equal to 0.22 pounds per cubic foot.

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