Volume of Cones Examples

A right cone has a diameter of 6 m and a height of 12 m. What is its volume?

Applying the volume formula for cones right from the get-go should do the trick. Of course, we should already know that radius is half the diameter, or 3 in this case.

V = ⅓πr²h
V = ⅓π(3 m)²(12 m)
V ≈ 113.1 m³

A cone has been removed from the inside of a square pyramid. If the diameter of the cone's base has the same length as the pyramid's base, what's the volume of the resulting solid?

If we subtract the volume of the cone from the volume of the pyramid, we'll calculate the remaining volume of the weird-looking solid that's left. To do that, we'll start with pyramid.

V_p = 2560 yd³

That's the volume of the entire pyramid. To de-cone it we'll need to calculate the cone's volume, too. The side of the pyramid's edge is the diameter of the circle, but we're using the radius, which is half of the edge.

V_c ≈ 2010.6 yd³

The final frontier. Subtract the volume of the cone from the volume of the pyramid.

V = V_p – V_c
V = 2560 yd³ – 2010.6 yd³
V = 549.4 yd³

We're not sure why that's useful, but there you go.