Question Video: Calculating the Density of a Sphere Mathematics

A sphere with a radius of 10 feet has a density of 8 lb/ft³. Work out, to the nearest pound, the mass of the sphere, knowing that density = mass/volume.

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Video Transcript

A sphere with a radius of 10 feet has a density of eight pounds per cubic foot. Work out, to the nearest pound, the mass of the sphere, knowing that density equals mass divided by volume.

As density is equal to mass divided by volume, the mass must be equal to the density multiplied by the volume. We are told in the question that the density of a sphere is eight pounds per cubic foot. We are not given the volume of the sphere, but we are given its radius.

The volume of any sphere is equal to four-thirds 𝜋𝑟 cubed. If the radius is equal to 10 feet, we can substitute 𝑟 equals 10 into this formula. 𝑉 or the volume is therefore equal to four-thirds multiplied by 𝜋 multiplied by 10 cubed. 10 cubed is equal to 1000. This means that 𝑉 is equal to 4000𝜋 over three.

Whilst we could type this into the calculator, it is better to round our answer at the end for accuracy. The volume of the sphere is 4000𝜋 over three cubic feet.

We can now calculate the mass 𝑚 by multiplying eight by 4000𝜋 over three. This is equal to 32000𝜋 over three. Typing this into the calculator gives us 33510.32 and so on. As the three after the decimal point is less than five, we need to round down.

The mass of the sphere to the nearest pound is 33510 pounds. This can also be written as it was in the question as lbs.

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