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lora16 [44]
3 years ago
13

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
Mathematics
2 answers:
anzhelika [568]3 years ago
8 0
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
Feliz [49]3 years ago
4 0

Answer:

R=r* \sqrt{3}

Step-by-step explanation:

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

The formula for the volume is = \frac{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} =\frac{1}{3} R^{2}

so, R^{2} =3r^{2}

R=\sqrt{3r^{2} }

R=r* \sqrt{3}

This is the final answer.

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