Question

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x- axis is an equilateral triangle, the. It's volume is..

Answer 1

??? couldn't picture at all

Answer 2

*then, it's volume is ...

Answer 3

imagine a bunch of triangles popping out in the z-direction

Answer 4

circle: x^2 + y^2 = 9
--> y = sqrt(9-x^2)

volume is sum of all the areas of the triangles
area = sqrt3/4 *(2y)^2 = sqrt3 y^2 = sqrt3(9-x^2)
\[V = \sqrt{3}\int\limits_{-3}^{3}(9-x^{2}) dx\]