The base of a solid is the circle x^2+y^2=9. Cross sections of the solid perpendicular to the x-axis are semi-circles. What is the volume, in cubics units, of the solid?

Question

a) 9 π/4
b) 18π
c) 9π
d) 72π

Answer 1

Steve posted this solution in 2016 : )
each square of thickness dx has side 2y, so its area is 4y^2.

Adding up all the thin squares, and using symmetry,

v = 2∫[0,3] 4(9-x^2) dx

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