Question

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.

Answer 1

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.