Question

To calculate the volume of the cone, the height is still needed. If the cone has a lateral surface with a length of 13 units, what is the height of the cone? (l is the length of the lateral surface; if you know this and the radius, what theorem can you use to find the height?)

Answer 1

`\Rightarrow h=√(169-r^2)` will be used to find the height of the cone.

Explanation:

We have been given the cone:

Length is given 13 units.

By pythagoras theorem:

`hypotenuse^2=length^2+radius^2`

`l^2=h^2+r^2`

We need to find the height

`h^2=l^2-r^2`

`\Rightarrow h^2=13^2-r^2`

`\Rightarrow h=√(169-r^2)` will be used to find the height of the cone.

Answer 2

The theorem is Pythagoras theorem.

Explanation:

Given the cone has a lateral surface with a length of 13 units. To find the volume of cone, the height is needed then we have to tell the theorem which is used to find the height if radius is known.

As the triangle AOB form a right angled triangle and if the slant height i.e l and radius r is known then in order to find height we can apply the Pythagoras theorem which can be stated as

The square of side hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides of the triangle.

`AB^2=AO^2+OB^2`

⇒
`l^2=r^2+h^2`

⇒
`h^2=l^2-r^2`

⇒
`h=\sqrt (l^2-r^2)`