Answer:
(b) 86.8 ft³
Explanation:
You want the volume of a cone with a slant height of 8 ft and a vertex angle of 50°.
Radius
The radius of the cone will be ...
Sin = Opposite/Hypotenuse
sin(25)° = radius/(8 ft)
radius = (8 ft)·sin(25°)
Height
The height can be found from ...
Cos = Adjacent/Hypotenuse
cos(25°) = height/(8 ft)
height = (8 ft)·cos(25°)
Volume
The volume of the cone is given by ...
V = 1/3πr²h
V = 1/3π(8·sin(25°))²(8·cos(25°)) ≈ 86.8 . . . . cubic feet
The volume of the cone is about 86.8 cubic feet.
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