Answer:
[tex]\pi\dfrac{12.1}{3}\left(\dfrac{12.1}{\tan 57^{\circ}}\right)^2[/tex]
Step-by-step explanation:
You are interested in two of the sides of the right triangle, the leg AC and the leg BC. The trig function that relates their values to the angle shown is told you by the mnemonic SOH CAH TOA, which reminds you ...
Tan = Opposite/Adjacent
The side opposite the angle, BC is given as 12.1; the side adjacent is AC, designated r. Then the above relation tells you ...
tan(57°) = 12.1/r
Rearranging, we have ...
r = 12.1/tan(57°)
The volume of the cone is given by the formula ...
V = (1/3)πr²h . . . . . where h = 12.1
Filling in what we know, this is ...
V = (1/3)π(12.1/tan(57°))²·12.1
This can be rearranged to the form shown in your answer choices:
V = π(12.1/3)(12.1/tan(57°))² . . . . . . matches the lower-right choice
