Interpretation : Two methods to determine the volume when height of water is given are to be explained.
Concept Introduction : Meteorologists keep track of the amount of rainfall by measuring the height of rain water collected in rain gauge.
Answer to Problem 1E
Method 1
Method 2 (Usingproportional relationship)
Wherek is a proportionality constant.
(in case of rain gauge, the proportionality constant is also equal to the area of the base)
Explanation of Solution
Given information:
A cylindrical rain gauge has an area of 2.0 cm2 and height of water is 3.0 cm.
Amount of rainfall can be measured using an instrument called rain gauge.
Method 1 (Mathematical calculation)
(since the rain gauge is cylindrical)
Method 2 (Usingproportional relationship)
Height and volume for a specific rain gauge are related by a proportionality constant, k .
The relation can be depicted as:
Wherek is a proportionality constant.
(In case of rain gauge, the proportionality constant is also equal to the area of the base)
Volume and height are proportional for containers with uniform shape and parallel walls.
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