Question

Okay that's fine the volume of the figure in cubic yards.

Answer 1

We are asked to find the volume of the cone.

Recall that the volume of a cone is given by

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

Where r is the radius and h is the height of the cone.

As you can notice, we are not given the height of the cone but instead, we are given the slant length.

So, let us first find the height of the cone.

As you can see, we can use the Pythagorean theorem to find the height (h)

`\begin{gathered} r^2+h^2=L^2 \\ 9.6^2+h^2=26.5^2 \\ h^2=26.5^2-9.6^2 \\ h^2=702.25-92.16 \\ h^2=610.09 \\ h=\sqrt[]{610.09} \\ h=24.7\: yd \end{gathered}`

So, the height of the cone is 24.7 yards.

Now let us find the volume of the cone

`\begin{gathered} V=(1)/(3)\cdot\pi\cdot r^2\cdot h \\ V=(1)/(3)\cdot\pi\cdot9.6^2\cdot24.7 \\ V=(1)/(3)\cdot\pi\cdot92.16^{}\cdot24.7 \\ V=2383.79\: yd^3 \end{gathered}`

Therefore, the volume of the given figure is 2383.79 cubic yards.

The 1st option is the correct answer.