Asked by Anonymous
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.
Answers
Answered by
oobleck
The hypotenuse of the triangle is the line y = (a-x)/2
That means the diameter of the semicircle at (x,y) is y, so the area is
π/4 y^2 = π/4 (a-x)^2/4
The volume is thus
v = ∫[0,a] π/16 (a-x)^2 dx
That means the diameter of the semicircle at (x,y) is y, so the area is
π/4 y^2 = π/4 (a-x)^2/4
The volume is thus
v = ∫[0,a] π/16 (a-x)^2 dx
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.