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 eh - 1.
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 eh - 1.
Find the volume of water in the tank when h = 3.
V = ∫03(eh - 1) dh
= [eh - h]03 - [2]
= e3 - 3 - [e0 - 0]
= e3 - 3 - 1 - [3]
= e3 - 4
[1]
Set the cross sectional area S(h) = eh - 1.
The level h moves from 0 to 3.
The level h moves from 0 to 3.
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