Asked by dee
The base of a solid is the region bounded by the parabola x^2 = 8y and y=4. Each cross section perpendicular to the y-axis is an equilateral triangle. Find the volume.
Answers
Answered by
Steve
Let's use a little symmetry here.
So, we have the base with length 2x and height x√3. That means if we add up all the thin slices, the volume is
v = ∫[0,8] (1/2)(2x)(x√3) dy
= ∫[0,8] √3 x^2 dy
But x^2 = 8y, so
v = ∫[0,8] 8√3 y dy
now just crank it out
So, we have the base with length 2x and height x√3. That means if we add up all the thin slices, the volume is
v = ∫[0,8] (1/2)(2x)(x√3) dy
= ∫[0,8] √3 x^2 dy
But x^2 = 8y, so
v = ∫[0,8] 8√3 y dy
now just crank it out
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