Video: Converting Units to Solve Density Problems

The cylinder in the given figure has a mass of 12400 kg. Work out the density of the cylinder in kilograms per cubic meter, giving your answer accurate to three significant figures. Hint : Density = Mass/Volume.

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Video Transcript

The cylinder in the given figure has a mass of 12400 kilograms. Work out the density of the cylinder in kilograms per cubic metre, giving your answer accurate to three significant figures. And then there’s a hint. Density equals mass divided by volume.

Well, that’s great. We’re looking to calculate the density. And we’re told that, to do so, we need to divide the mass by the volume. We’re even told that the mass of the cylinder in kilograms is 12400. And since we’re looking to calculate the density in kilograms per cubic metre, we can leave this in kilograms.

We are, however, going to need to calculate the volume of the cylinder. And so we recall the formula for the volume of a prism. It’s the area of the cross section multiplied by its perpendicular height. Now of course, we’re working with a cylinder. And the cross section of a cylinder is a circle. The area of the circle is 𝜋𝑟 squared. So the volume of a cylinder is 𝜋𝑟 squared ℎ, where 𝑟 is the radius and ℎ is the height.

The radius of our cylinder is four metres, and its height is six. So the volume is 𝜋 times four squared times six, which is 96𝜋 cubic metres. Since we know density is equal to mass divided by volume, we can simply divide the mass — that’s 12400 — by the volume — that’s 96𝜋. That gives us 41.115 and so on, which when rounded to three significant figures is 41.1 kilograms per cubic metre.

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