Actually it isn't. That's the formula for a cylinder. A cone is 1/3 of that value.
Pi times Radius times Radius times height
The volume of a cone is one-third the base area times the height. It can also be written as the volume of a cone is one-third pi times the square of the radius of the base times the height.
the volume changes as radius squared and linear with height, so tripling radius and double of height gives 3 x 3 x 2 = 18 times more volume
A cone with a radius of 3 and a volume of 37.7 has a height of about 4 units.
A cone with height 18 and radius 6 has a volume of 678.6 units3
A cone with a radius of 8 and a height of 8 has a volume of 536.17 units3
A cone with a radius of 3 and height of 3 has a volume of 28.27 units3
Since the volume of a cone is proportional to the square of the radius (look at the formula), double the radius would mean four times the volume.
The volume of a cone is 1/3 pi times the radius squared times the height. When given the volume and height divide both sides by the height. Volume divided by height is equal to 1/3 times pi times the radius squared. Now divide both sides by 1/3 pi. This will leave you with the radius squared. Take the square root of both sides and you will get the radius.
If you look at the formulas for volume of a cone and volume of a cylinder you can see that a cone will fit in exactly three times if the height and radius of the cone and cylinder are equivalent. A cone has the equation: (1/3)*pi*(r^2)*h=Volume. And a cylinder has the equation: pi*(r^2)*h=Volume. With h equaling height and r equaling radius, you can see that 3*(Volume of a cone)=Volume of a cylinder. Therefore, the cone would fit in three times if height and radius are equivalent for the two figures.
A cone with height 8cm and radius 15cm has a volume of 1884.96cm3
A cone, when radius is 4 and height is 21, has a volume of 351.86 units3