SOLUTION: a cone of radius 3cm and slant height 6cm is cut into four identical pieces. calculate the total surface area of the four pieces

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Question 1176161: a cone of radius 3cm and slant height 6cm is cut into four identical pieces. calculate the total surface area of the four pieces
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The lateral surface area of a cone is %28pi%29%28r%29%28l%29 where l is the slant height. For this cone, that is %28pi%29%283%29%286%29+=+18pi.

The height of the cone is found as the other leg of a right triangle with one leg 3 and hypotenuse 6. That gives us h+=+3%2Asqrt%283%29.

After the cone is cut into four identical pieces, the total surface area of one piece includes...
(1) one-quarter of the area of the base of the cone;
(2) one-quarter of the lateral surface area of the cone; and
(3) two right triangular faces with legs 3 and 3*sqrt(3).

Do the calculations for one piece and multiply the total times 4....