Answered

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

Verified Answer :

Volume of a sphere is given by the formula: \(V_{\circ}=\frac43\pi r^3\)

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

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

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

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