A cone has a base radius of 6, and a lateral surface area of 12sqrt34*pi. Find the volume of the cone.
Lateral surface area =
pi * radius * slant height of cone
So
12√34 * pi = pi * 6 * slant height of cone [ divide out pi ]
12√34 = 6 * slant height of cone [divide both sides by 6 ]
2√34 = slant height of cone = √ [ 34 * 4 ] = √ 136
Using the Pythagorean Theorem......the height of the cone =
√[ (√136)^2 -6^2 ] = √ [136 - 36 ] = √100 = 10
So.....the volume of the cone is
(1/3) pi * radius^2 * height =
(1/3) pi (6)^2 * 10 =
(1/3) pi * 360 =
120 pi units^3