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

It will take 6 full cones to completely fill the cylinder with fluid.

The volume of a cylinder is given as ;

V = πr²h and

The volume of a cone is 1/3πr²h

Since they have thesame radius

r = r

let H be height of cylinder and h be height of cone

The height of cone = 1/2height of cylinder

h = 1/2H

Therefore;

Volume of cone = 1/3 × π × r ²× 1/2H

Volume of cone = πr²H/6

therefore

volume of cylinder = 6 × volume of cone

Answer 2

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 = }(1)/(3)\pi r^2h\text{ = }(1)/(3)\pi r^2*(h)/(2)\text{ = }(\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{ }/\text{ }(\pi r^2h)/(6) \\ =\text{ }\pi r^2h\text{ }*\text{ }(6)/(\pi r^2h) \\ \text{= 6} \end{gathered}`

Final answer

6 full cones