Engineering Board Exam Reviewer · Solid Geometry: Cones, Spheres, and Frustums · hard
A sector of radius 10 and central angle 216° is rolled into a cone. Find the volume of the cone.
- 120 π 376.99
- 48 π 150.8
- 288 π 904.78
- 96 π 301.59
Answer
D. 96 π 301.59
Solution
The arc length 216/360(2π)(10)=12π becomes the base circumference, so the base radius is 6. The slant height is 10, so the height is 8. V= 13π(36)(8)=96π 301.59.
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