A circle has a radius of 25. A circular sector, with an angle of 320 degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.
+128474 The radius of 25 will be the slant height of the cone
The circumference of the cone's base = 2pi (25) * 32 / 36 = 400pi / 9
The radius of the cone = (400pi / 9) / (2pi) = 400/18 = 200/9
Using the Pythagorean Theoren, the height of the cone = sqrt ( 25^2 - (200/9)^2 ) = (25./9)sqrt 17
Volume of cone = (1/3)pi *[ 200/9]^2 * [ (25/9)sqrt 17 ] ≈ 5922.8 units^3
