Question

he radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters. The number of times one needs to use the completely filled cone to completely fill the cylinder with water is?

Answer 1

Volume of cylinder: $V_{\text{cyl}}=\pi r^2h$, where $r$ is the radius and $h$ is the height. This volume is $\pi\times10^2\times20=2000\pi$ (cubic cm).

Volume of cone: $V_{\text{cone}}=\dfrac13\pi r^2h$, with the same variables denoting the same parameters. This volume is $\dfrac13\pi\times5^2\times10=\dfrac{250}3\pi$ (also cubic cm).

The number of times it would take to fill the cylinder with water using the cone as a source would be

$\dfrac{2000\pi}{\dfrac{250}3\pi}=24$