Chapter U3.2, Problem 7E

(a)

Interpretation Introduction

Interpretation: The rainstorm which dropped the most rain needs to be determined on the basis of given data:

Strom number	Height	Volume (cm3)
1	1 cm	2.5
2	2.5 cm	6.3
3	0.5 cm	1.1
4	8 cm	20.0
5	5 cm	12.5

Concept Introduction: The dimensional analysis is the method to convert one unit to another with the help of convertor factor.

The conversion factor represents the relation between two units and is used to convert one to another. Both Inch and centimeter are units of length and can be converted into each other whereas cm³ is the unit of volume.

Answer to Problem 7E

Storm 4 dropped most of rain because the volume is maximum in storm 4. Thus, volume and height are used to determine the storm with most rain.

Explanation of Solution

Given:

Strom number	Height	Volume (cm3)
1	1 cm	2.5
2	2.5 cm	6.3
3	0.5 cm	1.1
4	8 cm	20.0
5	5 cm	12.5

According to given data the storm number 4 dropped most of rain. This is because volume is highest in storm 4 that is 20.0 cm³.

(b)

Interpretation Introduction

Interpretation: The pattern in the rainstorm needs to be determined with below data.

Strom number	Height	Volume (cm3)
1	1 cm	2.5
2	2.5 cm	6.3
3	0.5 cm	1.1
4	8 cm	20.0
5	5 cm	12.5

Concept Introduction: The dimensional analysis is the method to convert one unit to another with the help of convertor factor.

The conversion factor represents the relation between two units and is used to convert one to another. Both Inch and centimeter are units of length and can be converted into each other whereas cm³ is the unit of volume.

Answer to Problem 7E

The volume of rain increases from storm 1 to storm 5 therefore it is an increasing pattern.

Explanation of Solution

Given:

Strom number	Height	Volume (cm3)
1	1 cm	2.5
2	2.5 cm	6.3
3	0.5 cm	1.1
4	8 cm	20.0
5	5 cm	12.5

According to given data the volume of rain and height increase from storm 1 to 5. Therefore it exhibits the increasing pattern.

(c)

Interpretation Introduction

Interpretation: The graph between height and volume that show the proportionality of height with volume needs to be drawn.

Strom number	Height	Volume (cm3)
1	1 cm	2.5
2	2.5 cm	6.3
3	0.5 cm	1.1
4	8 cm	20.0
5	5 cm	12.5

Concept Introduction: The dimensional analysis is the method to convert one unit to another with the help of convertor factor.

The conversion factor represents the relation between two units and is used to convert one to another. Both Inch and centimeter are units of length and can be converted into each other whereas cm³ is the unit of volume.

Answer to Problem 7E

  

Explanation of Solution

Given:

Strom number	Height	Volume (cm3)
1	1 cm	2.5
2	2.5 cm	6.3
3	0.5 cm	1.1
4	8 cm	20.0
5	5 cm	12.5

According to given data the graph between height and volume is as given below;

  

The straight line in curve reflects that with increase in height, the volume of rain increase. Thus height is directly proportional to volume of rain.

(d)

Interpretation Introduction

Interpretation: The reason for all the data points to not lie exactly on a straight line needs to be explained.

Storm number	Height	Volume (cm3)
1	0.5 cm	1.1
2	1 cm	2.5
3	2.5 cm	6.3
4	5 cm	12.5
5	8 cm	20.0

Concept Introduction: The dimensional analysis is the method to convert one unit to another with the help of convertor factor.

The conversion factor represents the relation between two units and is used to convert one to another. Both Inch and centimeter are units of length and can be converted into each other whereas cm³ is the unit of volume.

Answer to Problem 7E

In the given graph, all the data points do not all lie exactly on a straight line because with the height is not increasing in exact proportion of volume of rain fall.

Explanation of Solution

According to given data the graph between height and volume is as given below;

  

Strom number	Height	Volume (cm3)
1	0.5 cm	1.1
2	1 cm	2.5
3	2.5 cm	6.3
4	5 cm	12.5
5	8 cm	20.0

In the given graph, all the data points do not all lie exactly on a straight line because with the height is not increasing in exact proportion of volume of rain fall.

(e)

Interpretation Introduction

Interpretation: The volume of rainfall at 6.0 cm height needs to be determined.

Storm number	Height	Volume (cm3)
1	0.5 cm	1.1
2	1 cm	2.5
3	2.5 cm	6.3
4	5 cm	12.5
5	8 cm	20.0

Concept Introduction: The dimensional analysis is the method to convert one unit to another with the help of convertor factor.

The conversion factor represents the relation between two units and is used to convert one to another. Both Inch and centimeter are units of length and can be converted into each other whereas cm³ is the unit of volume.

Answer to Problem 7E

At 6.0 height = 15.0 cm³ volume

Explanation of Solution

According to given data the graph between height and volume is as given below;

  

In the platted graph, at height 6.0 cm, the volume of rain fall is 15.0 cm³.