Chapter U3.54, Problem 8E

Interpretation Introduction

Interpretation : Whether the given cup would make for a good rain gauge or not is to be decided.

Concept Introduction : After a rainfall, rain can be several inches deep at some places or it may not be so deep on the sidewalks. Rain can be measured using rain gauge. Meteorologists keep track of the amount of rainfall by measuring the height of rain water collected in rain gauge.

Answer to Problem 8E

No, the given cup would not make for a good rain gauge because it does not have parallel walls and uniform shape.

Explanation of Solution

Given information:

The following cup is given to be used as a rain gauge.

Meteorologists keep track of the amount of rainfall by measuring the height of rain water collected in rain gauge in a particular time period. They use height and not volume to report rainfall. Volume and height are related to each other by a number called proportionality constant. In case of rain gauge this constant is equal to the area of the base of container.

Volume and height are proportional for containers with uniform shape and parallel walls. The given cup does not have uniform shape and parallel walls so it cannot be used to measure rainfall. Its volume would vary at different heights.

Conclusion

Volume and height for a specific rain gauge are related by a proportionality constant, k.