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?

Verified Answer :

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

\(\dfrac{2000\pi}{\dfrac{250}3\pi}=24\)