Question

I need to find the volume of these two shapes

Answer 1

We have to find the volume of the cone, knowing the height of the cone (h=11 ft) and the radius of the base of the cone (r=7 ft).

The volume of a cone can be expressed as:

`V=(1)/(3)\pi r^2h`

Then, we can replace the values and calculate:

`\begin{gathered} V=(1)/(3)\pi r^2h \\ V=(1)/(3)\pi\cdot7^2\cdot11 \\ V=(1)/(3)\pi\cdot49\cdot11 \\ V=(539\pi)/(3) \\ V\approx564.44 \end{gathered}`

The volume of the cone is approximately 564.44 ft^3.

For the sphere, we know the radius (r=22 yd).

The expression for the volume of a sphere is:

`\begin{gathered} V=(4)/(3)\pi r^3 \\ V=(4)/(3)\pi\cdot22^3 \\ V=(4)/(3)\pi\cdot10648 \\ V=(42592\pi)/(3) \\ V\approx44602.24 \end{gathered}`

The volume of the sphere is approximately 44602.24 yd^3.

Answer:

Volume cone = 564.44 ft^3

Volume sphere = 44602.24 yd^3