Region R is bounded by the curves y = 4x^2 and y = 4. A solid has base R, and cross sections perpendicular to the y-axis are sem
icircles with the diameter lying in R. The volume of this solid is
A. pi/4
B. pi/2
C. pi
D. 2pi
1 answer:
Each cross section has a diameter equal the horizontal distance between the two "halves" of the parabola. We have
y = 4x² ⇒ x = ±√y/2
so the diameter for some given y would be √y/2 - (-√y/2) = √y.
The volume of a cross section with thickness ∆y is then
π/2 (√y/2)² ∆y = π/8 y ∆y
The total volume of the solid would then be
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