# Area and Volume of a Cone

Instructions: Enter the radius $$r$$ and the height $$h$$ of a cylinder and the units (cm, mt, ft, etc) and the solver will compute the corresponding area and volume of the given cone.

Type the radius of the cone $$r$$ =

Type the height of the cone $$h$$ =

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

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.

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