Hello, chibiusagi!
A drinking glass has the shape of a truncated cone.
If the radii of the base and the top are 3 cm and 4 cm respectively
and the depth is 10 cm, (a) find by intergration, its capacity.
(b) If the glass is filled with water to a depth of 5 cm,
find the volume of the water.
Turn the glass 90°; the diagram looks like this: Code:

 *(10,4)
 * 
 * 
3 * 
 
 
 
   *      *  
 10
The equation of the line is: .$\displaystyle y \:=\:\frac{1}{10}x + 3$
The region bounded by the line, the xaxis, the yaxis, and $\displaystyle x=10$
. . is revolved about the xaxis.
(a) The total volume is: .$\displaystyle V \;=\;\pi\int^{10}_0\left(\frac{1}{10}x+3\right)^2\ ,dx$
(b) The volume of the water is: .$\displaystyle V \;=\;\pi\int^5_0\left(\frac{1}{10}x+3\right)^2\,dx $