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)=(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!