Work out the volume of the sphere, giving
your answer accurate to two decimal places.
First, we remember the formula we need
for calculating the volume of a sphere. It’s four-thirds 𝜋𝑟 cubed, where 𝑟 is
the radius of the sphere. We can see from the diagram that the
radius of this sphere is 6.3 centimeters. That’s the distance from any point on the
sphere’s surface to the center of the sphere. So we can substitute this value of 𝑟
directly into our formula, giving that the volume of this sphere is equal to four-thirds 𝜋
multiplied by 6.3 cubed.
We must remember that it is only the
radius that we are cubing, so only the value of 6.3, not the factors of four-thirds and
𝜋. As we’ve been asked to give our answer
accurate to two decimal places, it’s reasonable to assume that we can use a calculator. So evaluating this on our calculators
gives 1047.394424 continuing.
In order to round our answer to two
decimal places, we need to consider the value in the third decimal place. It is a four. And as this is less than five, this tells
us that we’re rounding down. So we have a value of 1047.39. The units of volume will be cubic
units. And as the units given for the radius
were centimeters, the units for the volume will be cubic centimeters. And so we have our answer to this
problem. The volume of the sphere, given to two
decimal places, is 1047.39 cubic centimeters.