The base of a solid is the circle x^2 + y^2 = 9. cross sections of the solid perpendicular to the x-axis are equilateral triangles. what is the volume, in cubic units, of the solid?
36 times the square root of 3
36
18 times the square root of 3
18

Recall that the area of an equilateral triangle with side length is .

In the plane, the base is given by two equations:

so that for any given , the vertical distance between the two sides of the circle is

and this is the side of length of each triangular cross-section for each . Then the area of each cross-section is

and the volume of the solid is

∈3,600

step-by-step explanation: