Question

s:Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar and ^ to indicate an exponent. 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

Vco = 1/3×πr2h
Vcy = Vco --> πr^2×h = 1/3πR^2×h
h's cancel, as well as π's
r^2 = 1/3R^2 --> R^2 = 3r^2 -->
SR (R^2) = SR (3r^2)
R = SR(3)×r

Answer 2

`R=r* √(3)`

Explanation:

The formula for the volume of a cylinder is V =
`\pi r^(2) h`

The formula for the volume is =
`(1)/(3)\pi r^(2) h`

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

Equating both radii:

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

so,
`R^(2) =3r^(2)`

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

`R=r* √(3)`

This is the final answer.