Question:

Find a formula for the volume of this trapezoid (rotates 360 degrees around the x-axis):

R= big radius

r= small radius

h= height

The area is equal to:

$\displaystyle A=\frac{1}{2}\cdot(r+R)\cdot h$

Volume of an object rotating around the x-axis:

$\displaystyle V_x=\pi\cdot\int_{a}^{b}f(x)^2\, dx$

Judging by the graph, it starts from x=0, and it ends on x=h, therefore the interval is [0;h].

The area function is the equation for a trapezoid, therefore, the function.

Conclusion:

$\displaystyle V_x=\pi\cdot\int_{0}^{h}(\frac{1}{2}\cdot(r+R)\cdo t h)^2\, dh$

Did I solve this correctly? I'm afraid, the "dh" is wrong, and generally just unsure if I solved this correctly.