How to Compute the Surface Area and Volume of a Cone?

This volume of a cone calculator with steps will do the calculation for you. In order to compute the area and volume of a right circular cone of radius \(r\) and height \(h\) we use the following formulas:

\[ \text{Area} = \pi r (r + \sqrt{h^2 + r^2})\] \[ \text{Volume} = \frac{r^2 h\pi}{3} \]

Computationally speaking, it is fairly simple to compute the area and the volume of a cone, by simply plugging the radius \(r\) and height \(h\) in the above formulas. For example, if the radius is \(r = 3\) and the height is \(h = 4\), we compute

\[ \text{Area} = \pi r (r + \sqrt{h^2 + r^2}) = 3\pi (3 + \sqrt{4^2 + 3^2}) = 24\pi\] \[ \text{Volume} = \frac{r^2 h\pi}{3} = \frac{3^2\cdot 4 \pi}{3} = 12\pi \]

which completes the calculation.

How to deal with other shapes?

Each geometric type of shape will have a specific treatment. You can try our cube calculator to get the surface area and volume of a cube, among many other shapes