### 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.

Letβs begin by drawing a sketch of
the cone. We are told that the diameter of
the circular base is equal to 10.5. The height of the cone is 11.3. This is the perpendicular distance
from the apex to the base. Note that the question does not
tell us whether this is a right cone or an oblique one, but in fact it does not
matter, since we have been given the perpendicular height. When using the perpendicular
height, our formula for volume is applied in the same way to both cases.

In order to calculate the volume of
any cone, we use the formula one-third ππ squared multiplied by β, where π is the
radius of the circular base. We know that the radius of any
circle is half its diameter, and we are told the diameter is 10.5. The radius is, therefore, equal to
a half multiplied by 10.5. This is equal to 5.25. We can now substitute our values
for the radius and height into the formula.

The volume of the cone is 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 are asked to give our solution
correct to two decimal places. As the deciding number is a six, we
round up, giving us an answer of 326.16. Volume is measured in cubic
units. And as there were no length units
given for the diameter or the height, the volume is equal to 326.16 cubic units.