Question

Use the diagram below to determine which has the greater volume, the cone or the cylinder. 4 cm 6 cm 6 cm | 0 cm A The cylinder has the greater volume. (B) The cone has the greater volume. The cylinder and the cone have equal volume. D.) The volumes can not be determined.

Answer 1

Let's find the volume of each figure.

The volume of the cylinder is given by:

`Vc=\pi\cdot r^2_{}\cdot h`

Where:

r = radius = 4cm

h = height = 6cm

so:

`Vc=\pi\cdot(4^2)\cdot(6)=96\pi\approx301.6cm^2`

The volume of the cone is given by:

`V_(cn)=(1)/(3)\pi\cdot r^2\cdot h`

where:

r = radius = 6cm

h = height = 8cm

so:

`\begin{gathered} V_(cn)=(1)/(3)\pi\cdot(6^2)\cdot(8) \\ V_(cn)=96\pi\approx301.6cm^2 \end{gathered}`

Since:

`V_c=V_(cn)_{}`

The cylinder and the cone have equal volume.