How Do You Calculate the Volume of a Solid Revolved Around the X-Axis?

[Theorotical]

Homework Statement

Fine the volume of the solid generated by revolving the "triangular" region bounded by the x-axis, the line x=PI/3, and the curve y=tanx in the first quadrant about the x-axis.

Homework Equations

volume of revolution using disk method =integration (PI*[r(x)]squared dx) also using the shell and washer method

The Attempt at a Solution

i have tried to sketch but the problem is how to express the line PI/3 in numbers, also when i integrate using the following method:
V=int.[from 0 to root 3][PI*(root 3 -tanx)squared] dx

the problem gets more complicated and i feel frustrated as my exam is tom. and am really scared from these kind of problems, so please help me

 

[Dick]

Where did 'root 3' come from? x=pi/3 is a vertical line through (pi/3,0). The x-axis is a horizontal line through (0,0). y=tan(x) is a curve connecting (0,0) and (pi/3,tan(pi/3)). Draw them. You are integrating along x. What is r(x) as a function of x?