cone

A cone is a three-dimensional shape. It is a specific type of pyramid with a circular base. The apex of the cone is directly above the centre of the circle.

The formula for the volume of a cone is:

      Volume = \frac{1}{3} \times\pi\times r^{2} \times h

V = \frac{1}{3} \pi r^{2} h

In this formula r represents the radius of the circle (the base) and h represents the height of the apex above the centre of the circle.

The formula for the area of the base of a cone is the same as for the area of a circle:

      Area = \pi \times r^{2}

A = \pi r^{2}

The formula for calculating the area of the curved surface of a cone is:

      Area = \pi \times r \times l

A = \pi r l

In this formula l represents the length of the cone’s slant. This is the distance from the apex to any point on the circumference of the circle or base. Knowing the radius r of the circle and the height h of the cone, we can use Pythagoras’ theorem to calculate l:

    l = \sqrt{(r^{2}+h^{2})}