What is the volume of this cone?

The volume of the cone is approximately 453.0 cm³

Step-by-step explanation:

The volume of a cone is one third that of a cylinder with the same height and radius.  That gives us  1/3 πr²h, where r is radius and h is height.

However, we are not given the height of the cone, but the side length.  We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length.  You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:

So we can find the height of the cone with that:

Now that we have the cone's height, we can solve for its volume: