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

A) 36

B) 12sqrt3

C) 18sqrt3

D) 24sqrt3

E) 36sqrt3

The correct answer was E. Hoping someone could explain how that is.

Letter E is correct.

Area of equilateral trianlge = (1/2) tiime a^2 square root 3

Equation for the base is = x^2+y^2 = 9

at x,

y = square root (9-x^2)

Side of triangle a = 2y

d times Volume = (1/2) a^2 square root 3 dx

d times V = (square root 3) (9-x^2) dx

V = square root 3 INT (9-x^2) dx

-3V = 2square root INT (9-x^2) dx

0

V = 2 square root 3 (9x-x^3/3)

V=2 square root 3 (27-9)

V = 36 square root 3

The answer is E.