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.