# Volume from its Cross Sectional Area

See how to find the volume from its cross sectional area.

1 example and its solution.

## Volume from its Cross Sectional Area

### Formula

### Example

Water is filled into a tank below.

If the level of water is h,

then the surface area of water is e

Find the volume of water in the tank when h = 3.

Solution If the level of water is h,

then the surface area of water is e

^{h}- 1.Find the volume of water in the tank when h = 3.

V = ∫03(e

^{h}- 1) dh

= [e

^{h}- h]03 - [2]

= e

^{3}- 3 - [e

^{0}- 0]

= e

^{3}- 3 - 1 - [3]

= e

^{3}- 4

[1]

Set the cross sectional area S(h) = e

The level h moves from 0 to 3.

^{h}- 1.The level h moves from 0 to 3.

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