A circular sector with a radius of $25$ and a central angle of $345.6^\circ$ is rolled to form a cone. Find the volume of the cone.
Please help!
+128474 The radius will form the "slant height" of the cone
The arc length of the sector will form the circumference of the cone
This is 2*pi (25) (345.6 / 360) = 48pi units
The radius of the cone can be found as
Circumference = 2pi * r
48 pi = 2pi * r
48 = 2r
r = 24
The height of the cone = sqrt [ slant height^2 - radius^2 ] =
sqrt [ 25^2 - 24^2 ] =
sqrt [625 - 576] = sqrt [49] = 7
Volume (cone) = (1/3) pi * r^2 * height = (1/3)pi ( 24)^2 ( 7) = 1344 pi units^3
