Question

In a cone with a slant height of 6 feet, the slant height forms a 42 degree angle with the radius. Find the volume of the cone. Show all work.

Answer 1

ok see the volume of a cone is :\[1/3 \pi r^2h\]

Answer 2

okay

Answer 3

Use trigonometric function to find to radius of the circle (there is a triangle formed by the height and one vertice of the cone ) : then use the formula provided.

Answer 4

If the slant forms a 42 degree angle with the radius, the height of the cone will be equal to the sine of 42 degrees.

since of 42 degrees = .669130606
height/6 = .669130606
height of the cone = 4.015

Also, the radius will be equal to the cosine of 42 degrees
cosine of 42 degrees = .743144825
radius/6 = .743144825
radius = 4.459

Volume = 1/3 pi r^2 h
V = 1/3 (3.1415)(4.459)^2(4.015)
V = 1/3 (3.1415)(19.883)(4.015)
V = 1/3 (250.787)
V = 83.6 cubic feet

Note to above - (don't forget - it is cosine^2 - when you multiply by the cosine the second time, the 112 will be 83).

Hope that helps.