Chapter 8.4, Problem 36E

a.

To determine

To find:

The gradient between points A and B on the cinder cone using the given information. Include units in your answer.

Answer to Problem 36E

The gradient between points A and B on the cinder cone is 4000 feet per mile.

Explanation of Solution

Given:

A cinder cone is a type of volcano. To describe the steepness of a cinder cone from one point on cone to another, you can find the gradient between the two points.

  $\text{Gradient}=\frac{\text{Change in elevation (in feet)}}{\text{Horizontal change (in miles)}}$

The graph shows the cross section of a cinder cone.

  

Calculation:

We can see that point A is at (0,0) and point B is at (0.1,400). Upon substituting these values in gradient formula, we will get:

  $\begin{array}{l}\text{Gradient}=\frac{\text{Change in elevation (in feet)}}{\text{Horizontal change (in miles)}}\\ \text{Gradient}=\frac{\text{400}-0}{\text{0}\text{.1}-0}\\ \text{Gradient}=\frac{\text{400}}{\text{0}\text{.1}}\\ \text{Gradient}=\text{400}0\end{array}$

Therefore, the gradient between points A and B on the cinder cone is 4000 feet per mile.

b.

To determine

To find:

The gradient between points B and Con the cinder cone using the given information. Include units in your answer.

Answer to Problem 36E

The gradient between points B and C on the cinder cone is 1000 feet per mile.

Explanation of Solution

Given:

A cinder cone is a type of volcano. To describe the steepness of a cinder cone from one point on cone to another, you can find the gradient between the two points.

  $\text{Gradient}=\frac{\text{Change in elevation (in feet)}}{\text{Horizontal change (in miles)}}$

The graph shows the cross section of a cinder cone.

  

Calculation:

We can see that point B is at (0.1,400) and point C is at (0.2,500). Upon substituting these values in gradient formula, we will get:

  $\begin{array}{l}\text{Gradient}=\frac{\text{Change in elevation (in feet)}}{\text{Horizontal change (in miles)}}\\ \text{Gradient}=\frac{\text{500}-400}{\text{0}\text{.2}-0.1}\\ \text{Gradient}=\frac{\text{100}}{\text{0}\text{.1}}\\ \text{Gradient}=1\text{00}0\end{array}$

Therefore, the gradient between points B and C on the cinder cone is 1000 feet per mile.

c.

To determine

To find:

The gradient between points A and Con the cinder cone using the given information. Include units in your answer.

Answer to Problem 36E

The gradient between points A and Con the cinder cone is 2500 feet per mile.

Explanation of Solution

Given:

A cinder cone is a type of volcano. To describe the steepness of a cinder cone from one point on cone to another, you can find the gradient between the two points.

  $\text{Gradient}=\frac{\text{Change in elevation (in feet)}}{\text{Horizontal change (in miles)}}$

The graph shows the cross section of a cinder cone.

  

Calculation:

We can see that point A is at (0,0) and point C is (0.2,500). Upon substituting these values in gradient formula, we will get:

  $\begin{array}{l}\text{Gradient}=\frac{\text{Change in elevation (in feet)}}{\text{Horizontal change (in miles)}}\\ \text{Gradient}=\frac{\text{500}-0}{\text{0}\text{.2}-0}\\ \text{Gradient}=\frac{\text{500}}{\text{0}\text{.2}}\\ \text{Gradient}=\text{250}0\end{array}$

Therefore, the gradient between points A and Con the cinder cone is 2500 feet per mile.