volume of solids of revolution

**chibiusagi** · January 23rd 2008, 05:39 PM

A drinking glass has the shape of a truncated cone. IF the internal radii of the base and the top are 3 cm and 4 cm respectively and the depth is 10 cm, find by intergration, its capacity. If the glass is filled with water to a depth of 5 cm, fin the volume of the water.

I have done question related to intergration but only with the actual formula T_T so i can't work this out.

**Soroban** · January 23rd 2008, 08:12 PM

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: . $y \:=\:\frac{1}{10}x + 3$

The region bounded by the line, the x-axis, the y-axis, and $x=10$
. . is revolved about the x-axis.

(a) The total volume is: . $V \;=\;\pi\int^{10}_0\left(\frac{1}{10}x+3\right)^2\ ,dx$

(b) The volume of the water is: . $V \;=\;\pi\int^5_0\left(\frac{1}{10}x+3\right)^2\,dx$

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