Question

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

Answer 1

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!