Video Transcript
A steel ball has a radius of 10
centimeters. If the density of the ball is 8,000
kilograms per cubic meter, find the mass of the ball in kilograms. Give your answer to one decimal
place.
We are told that we have a ball
with radius 10 centimeters. The volume of any ball or sphere is
equal to four-thirds ๐๐ cubed. This means that we could calculate
the volume of the ball in cubic centimeters by substituting ๐ equals 10 into the
formula. As our units for density were
kilograms per cubic meter, we actually need to convert the radius into meters
first. As there are 100 centimeters in one
meter, 10 centimeters will be equal to 0.1 meters.
We can therefore calculate the
volume of the ball in cubic meters by multiplying four-thirds by ๐ by 0.1
cubed. Typing this into the calculator
gives us an answer of 0.004188 and so on. We were asked to calculate the mass
of the ball, which means this isnโt the final answer. We will therefore not round at this
stage.
We know that the density of any
object is equal to its mass divided by its volume. We can rearrange this formula so
that the mass is equal to the density multiplied by the volume. The mass of the ball will be equal
to 8,000 multiplied by 0.004188 and so on. This is equal to 33.5103 and so
on. Rounding to one decimal place, we
get an answer of 33.5. A steel ball with a radius of 10
centimeters, or 0.1 meters, and a density of 8,000 kilograms per cubic meter has a
mass of 33.5 kilograms.
