### Video Transcript

Find, in terms of π, the lateral
area of a right cone with base radius nine centimetres and height 13
centimetres.

Letβs begin by drawing a diagram of
the cone. Weβre told that the base radius is
equal to nine centimetres. The height of the cone, which goes
from the apex at the top to the centre or centroid of the base, is 13
centimetres. This creates a right-angled
triangle with a slant height π. The lateral area of a cone is the
area of its curved surface. This is equal to πππ. We multiplied π by the radius by
the slant height. We know that the radius of the cone
is nine centimetres. However, we donβt know the slant
height at present. We can, however, calculate this by
using Pythagorasβs theorem. This states that π squared plus π
squared is equal to π squared, where π is the length of the hypotenuse in a right
triangle.

In this question, π squared is
equal to nine squared plus 13 squared. Nine squared is equal to 81. 13 squared is equal to 169. 81 plus 169 is equal to 250. Therefore, π squared equals
250. Square-rooting both sides of this
equation gives us π is equal to root 250. Root 250 is equal to root 25
multiplied by root 10. As root 25 is equal to five, this
is equal to five root 10. The slant height of the cone is
five root 10 centimetres.

We can now substitute in this value
to calculate the lateral area. The lateral area is equal to π
multiplied by nine multiplied by five root 10. Nine multiplied by five root 10 is
45 root 10. As weβre asked to give our answer
in terms of π, this is equal to 45 root 10π. The lateral area of a right cone
with base radius nine centimetres and height 13 centimetres is 45 root 10π square
centimetres. Remember that our units for any
area or surface area are square centimetres, square metres, et cetera.