The base of solid is right triangle whose base side has length a and whose perpendicular side has length (1/2)a. Find the volume of the solid if cross sections perpendicular to the base the triangle are semicircles.
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1 answer

The hypotenuse of the triangle is the line y = (ax)/2
That means the diameter of the semicircle at (x,y) is y, so the area is
π/4 y^2 = π/4 (ax)^2/4
The volume is thus
v = ∫[0,a] π/16 (ax)^2 dx 👍
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answered by oobleck
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