A cylinder has a volume of 360 cubic centimeters. Find the volume of a cone with the same height and diameter as the cylinder.

Respuesta :

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The formula of a volume of a cylinder:

[tex]V_{cylinder}=\pi r^2H[/tex]

The formula of a volume of a cone:

[tex]V_{cone}=\dfrac{1}{3}\pi r^2H[/tex]

If a cone and a cylinder have the same radius and the same height, then a volume of a cylinder is three times greater than a volume of a cone.

[tex]V_{cylinder}=3V_{cone}\\\\V_{cone}=\dfrac{1}{3}V_{cylinder}[/tex]

[tex]V_{cylinder}=360\ cm^3[/tex]

[tex]V_{cone}=\dfrac{1}{3}\cdot360\ cm^3=120\ cm^3[/tex]

Answer: The volume of a cone is equal 120 cm³.