Video: Calculating Density given a Mass and Volume

Henry wants to work out the density of the soil in his garden. He fills a tub, with a capacity of 1.5 cubic feet, full of soil and tightly compacts it to remove as much air as he can. He weighs the soil and, after subtracting the mass of the tub, finds it has a mass of 124.5 pounds. What is the density of the soil?

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Video Transcript

Henry wants to work out the density of the soil in his garden. He fills a tub, with a capacity of 1.5 cubic feet, full of soil and tightly compacts it to remove as much air as he can. He weighs the soil and, after subtracting the mass of the tub, finds it has a mass of 124.5 pounds. What is the density of the soil?

We know that the density of any objects can be calculated by dividing its mass by the volume. You might have seen this set out in a triangle, as shown. In this question, our volume or capacity is measured in cubic feet. The mass of the soil is measured in pounds. This means that the units for density in this question will be pounds per cubic foot. The mass of the soil was 124.5 pounds and the capacity was 1.5 cubic feet. Therefore, the density will be equal to 124.5 divided by 1.5.

We could type this straight into the calculator. However, 1.5 is the same as the fraction three over two. Dividing by any fraction is the same as multiplying by the reciprocal of that fraction. So, 124.5 divided by three over two is the same as 124.5 multiplied by two-thirds. We can calculate this by firstly multiplying 124.5 by two. This is equal to 249. We can then divide 249 by the denominator of the fraction, in this case, three. 249 divided by three is equal to 83. Therefore, 124.5 multiplied by two-thirds is also 83.

The density of the soil in Henry’s garden is 83 pounds per cubic foot.

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