### Video Transcript

Work out the volume of a cone with
a diameter of 10.5 and a height of 11.3. Give your solution to two decimal
places.

Let’s begin by drawing a diagram of
the cone. We’re told that the diameter is
10.5. This is a distance from one side of
the circular base to the other, passing through the centre. The height of the cone is equal to
11.3. This is the distance from the apex
or top of the cone to the centre of the base. In order to calculate the volume of
a cone, we use the formula one-third 𝜋𝑟 squared multiplied by ℎ. At this stage, we know the height
of the cone, but we don’t know the radius.

The radius of the circular base is
the distance from the centre to the circumference of the circle. This is equal to half of the
diameter. Therefore, to calculate the radius,
we divide 10.5 by two. This is equal to 5.25. And we now have values for the
radius and height of the cone. Substituting in these values gives
us a volume equal to one-third multiplied by 𝜋 multiplied by 5.25 squared
multiplied by 11.3. Typing this into the calculator
gives us 326.1562 and so on. We were asked to round our solution
to two decimal places. As the six in the thousandths
column is greater than five, we will round up to 326.16. Volume is measured in cubic
units. As there are no specific units in
this question, the volume of the cone is equal to 326.16 cubic units.