calculus

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The base of a solid is a circle of
radius = 4
Find the exact volume of this solid if the cross sections perpendicular to a given axis are equilateral right triangles.

The equation of the circle is:
x^2 + y^2 = 16

I have the area of the triangle (1/2bh) to be equal to 2sqrt(12)

(1/2 * 4 * sqrt12)

there are triangles that have vertical bases. They run parallel to the y-axis. The triangles are inside of the circle

Any help would be greatly appreciated! Thanks!


The volume of a cone is
V =(1/3)*(base area)*(height)

In your equilateral case,
height = sqrt3 * r.
Therefore
V = sqrt3*pi*r^3

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