SOLUTION: The bases of a right cylindrical solid are each 135 degrees sectors of circles with a 4-inch radius each. The altitude of the solid is 12 inches. The the total surface area of thi

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Question 1197280: The bases of a right cylindrical solid are each 135 degrees sectors of circles with a 4-inch radius each. The altitude of the solid is 12 inches. The the total surface area of this solid may be expressed as T = d(pi + k) square inches. Find d + k.
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Not clear.
Is there a drawing?

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


I think the description is sufficiently clear. I see a tall cylindrical cake, originally with a radius of 4 inches and a height of 12 inches, from which several slices have been removed, leaving bases that are 135-degree sectors of the original circular bases. The surfaces of the "cake" are these:
(1) 2 bases that are 135-degree sectors of circles with radius 4;
(2) the curved lateral surfaces of the cake; and
(3) 2 rectangular surfaces where the cuts were made.

The areas of those surfaces are

(1) 2%28135%2F360%29%28pi%29%28r%5E2%29=%283%2F4%29%28pi%29%2816%29=12pi
(2) %28135%2F360%29%282pi%29%28r%29%28h%29=%283%2F8%29%282pi%29%284%29%2812%29=36pi
(3) 2%284%29%2812%29=96

The total surface area of the solid is 48pi%2B96

You can put that result in the prescribed form and answer the question.