SOLUTION: A cone whose base diameter and vertical height are 24cm and 5cm respectively is unfolded to form a sector of a circle.(a) calculate the radius of the sector (b)calculate the angle

Algebra ->  Surface-area -> SOLUTION: A cone whose base diameter and vertical height are 24cm and 5cm respectively is unfolded to form a sector of a circle.(a) calculate the radius of the sector (b)calculate the angle       Log On


   

Question 1022027: A cone whose base diameter and vertical height are 24cm and 5cm respectively is unfolded to form a sector of a circle.(a) calculate the radius of the sector (b)calculate the angle of the sector
Answer by josgarithmetic(39617) About Me  (Show Source):
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The base circumference will be missing from the unfolded circular surface. The radius of this unfolded circle will be same as slant height of the cone.

L=sqrt%28%2824%2F2%29%5E2%2B5%5E2%29
L=sqrt%28144%2B25%29
L=sqrt%28169%29
highlight%28L=13%29---------radius of this sector

If this unfolded part were a full circle, circumference would be 2%2Api%2A13=highlight%2826pi%29;

The circumference of the base: 2%2Api%2A%2824%2F2%29=24pi;
Angle of this sector is 360%28%2826-24%29%2F25%29=360%282%2F25%29=144%2F5=highlight%2828.8%2Adegrees%29.