Question

A cone has the same diameter as a cylinder but half the cylinder's height. How many full cones would it take to completely fill the cylinder with fluid? Explain.

Answer 1

Solution

Step 1

Given data

Cylinder

Diameter = d

Radius = r

Height = h

Cone

Diameter = d

Radius = r

Height = h/2

Step 2

$\begin{gathered} Volume\text{ of cylinder = }\pi r^2h \\ \\ Volume\text{ of a cone = }\frac{1}{3}\pi r^2h\text{ = }\frac{1}{3}\pi r^2\times\frac{h}{2}\text{ = }\frac{\pi r^2h}{6} \end{gathered}$

Step 3:

Divide the volume of a cylinder by the volume of a cone.

$\begin{gathered} \text{= }\pi r^2h\text{ }\div\text{ }\frac{\pi r^2h}{6} \\ =\text{ }\pi r^2h\text{ }\times\text{ }\frac{6}{\pi r^2h} \\ \text{= 6} \end{gathered}$

Final answer

6 full cones