document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #831744 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "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:
\n" ); document.write( "(1) 2 bases that are 135-degree sectors of circles with radius 4;
\n" ); document.write( "(2) the curved lateral surfaces of the cake; and
\n" ); document.write( "(3) 2 rectangular surfaces where the cuts were made.

\n" ); document.write( "The areas of those surfaces are

\n" ); document.write( "(1) $\"2%28135%2F360%29%28pi%29%28r%5E2%29=%283%2F4%29%28pi%29%2816%29=12pi\"$
\n" ); document.write( "(2) $\"%28135%2F360%29%282pi%29%28r%29%28h%29=%283%2F8%29%282pi%29%284%29%2812%29=36pi\"$
\n" ); document.write( "(3) $\"2%284%29%2812%29=96\"$

\n" ); document.write( "The total surface area of the solid is $\"48pi%2B96\"$

\n" ); document.write( "You can put that result in the prescribed form and answer the question.

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