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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

Respuesta :

budwilkins
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:

[tex]R=r* \sqrt{3}[/tex]

Step-by-step explanation:

The formula for the volume of a cylinder is V = [tex]\pi r^{2} h[/tex]

The formula for the volume is = [tex]\frac{1}{3}\pi r^{2} h[/tex]

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:

[tex]r^{2} =\frac{1}{3} R^{2}[/tex]

so, [tex]R^{2} =3r^{2}[/tex]

[tex]R=\sqrt{3r^{2} }[/tex]

[tex]R=r* \sqrt{3}[/tex]

This is the final answer.