To the nearest hundredth, what is the volume of a cone with a radius of 8 inches and a base angle of 60 degrees?

To find the volume of a cone, the formula used is:

[

V = \frac{1}{3} \pi r^2 h

]

where (V) is the volume, (r) is the radius, and (h) is the height of the cone.

Given that the radius (r = 8) inches, we first need to determine the height (h) of the cone using the base angle. The base angle given is (60) degrees. In a right triangle formed by the height, radius, and slant height of the cone, we can use trigonometric relationships to find the height.

In a right triangle, we can relate the height, the radius, and the angle as follows:

[

\tan(\theta) = \frac{h}{r}

]

Here, (\theta = 60) degrees and (r = 8) inches. Rearranging the above formula to solve for height (h):

[

h = r \tan(\theta) = 8 \tan(60^\circ)

]

Knowing that (\tan(60^\circ) = \sqrt{3}), we can calculate