Question

The formula for the volume of a cylinder is V=πr²h. The volume of a cylinder is three times the volume of a cone with the same radius and height. If the volume of a cone with the same height as a cylinder equals the volume of a cylinder, the equation for the radius of cone are in terms of the radius of cylinder R is______?

Answer 1

The formula for the volume of a cylinder is V=πr²h. The volume of a cylinder is three times the volume of a cone with the same radius and height.
Now, volume of cone is 1/3πh
`r^(2)`

If the volume of a cone with the same height as a cylinder equals the volume of a cylinder, the equation for the radius of cone in terms of the radius of cylinder R, is equal to 3R.
We get this by equating the volume of cone and cylinder:


`\pi R^(2) h = (1)/(3) \pi r^(2)h \\ \\ thus, r = 3R`