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 the cylinder, the equation for the radius of cone R in terms of the radius of cylinder r is

Answer 1

A on egde

Explanation:

Answer 2

Since both objects are assumed to have the same volume, matching the formulas we'll get:

π
`r^(2)`h =
`(1)/(3)`π
`R^(2)`h

Having both π and h at both sides of the equation, we can ignore them, so:


`r^(2)` =
`(1)/(3)`
`R^(2)`

And clearing R, according to the equation rules, we'll get:


`\sqrt[2]{3 r^(2) }` = R