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

Question

Mathematics

Johnny

6 May, 02:59

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

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Whitney · 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