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