Determine the volume of the right circular cone in terms of 𝜋.
The formula for the area of a cone is one-third times the radius squared times the height of the cone times 𝜋. Now, since it says to leave our answer in terms of 𝜋, this means we will leave the 𝜋 symbol in our answer. So we need to find the radius and the height.
The radius is found on the circle. And it goes from the center to a point on the circle. So our radius will be 20. Now, we can plug in 20 for 𝑟. Here, we can see the height of the cone. And that distance is actually over here on the left. The height is 24. So we can plug in 24 for ℎ.
So the first step that we need to take is we need to square 20. And 20 squared is 400. So if we multiply one-third times 400 times 24, we get 3200. Now, we can’t forget to bring down the 𝜋 as well as our units.
Now, our units are in centimetres. But this is a volume. So it should be centimetres cubed. Therefore, the volume of this cone is 3200 𝜋 cubic centimetres.