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your friend says that the volume of a sphere with a radius r is four times the volume of a cone with radius r. when is this true? Justify your answer

Respuesta :

Zepdrix
Volume of a sphere is given by the formula: [tex]V_{\circ}=\frac43\pi r^3[/tex]

If we pull the 4 out front we have, [tex]V_{\circ}=4\left(\frac13\pi r^3\right)[/tex].

Volume of a cone is given by the formula: [tex]V_{\triangle}=\frac{1}{3}\pi r^2\cdot h[/tex]

Notice that if the height of the cone is equal to the radius, [tex]V_{\triangle}=\frac13\pi r^2\cdot r[/tex]

then it's exactly what we see in our volume formula without the 4!

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