It is planned to create bench terraces on land with a 10% slope. With a vertical spacing of 2.5 meters between the terraces and a batter slope of 100%, determine both the working width (in meters) and the percentage of land area lost for cultivation.*

25.00 and 0.50

22.50 and 10.45

22.50 and 0.05

25.00 and 10.45

To solve the problem, let's break down the necessary steps to determine both the working width and the percentage of land area lost for cultivation.

### Given Information:
1. **Slope of the land (S)** = 10% (This means a vertical rise of 10 units for every 100 units of horizontal distance.)
2. **Vertical spacing between terraces (V)** = 2.5 meters
3. **Batter slope (b)** = 100% (This indicates a vertical rise of 1 unit for every 1 unit of horizontal distance, or a slope angle of 45 degrees.)

### Step 1: Calculate the Working Width (W)
The working width is the horizontal distance between the terraces. We can find it using the Pythagorean theorem.

1. **Horizontal Distance for Batter Slope (HB):**
   \[
   HB = V = 2.5 \text{ meters}
   \]

2. **Horizontal Distance due to Natural Slope (HS):**
   The slope is given as 10%. This implies that for every 1 unit rise vertically, there is 10 units horizontally.
   \[
   HS = \frac{V}{S} = \frac{2.5}{0.1} = 25 \text{ meters}
   \]

3. **Working Width (W):**
   Using the Pythagorean theorem, we get:
   \[
   W = \sqrt{(HB)^2 + (HS)^2} = \sqrt{(2.5)^2 + (25)^2}
   \]
   \[
   W = \sqrt{6.25 + 625} = \sqrt{631.25} \approx 25.12 \text{ meters}
   \]

Thus, the closest value for the working width is **25 meters**.

### Step 2: Calculate the Percentage of Land Area Lost for Cultivation
The area lost for cultivation can be found as follows:

1. **Width of bench (WB):**
   This is the actual horizontal distance that would be occupied by the terrace's riser.
   \[
   WB = V = 2.5 \text{ meters}
   \]

2. **Percentage of Land Area Lost:**
   \[
   \text{Percentage of land lost} = \frac{WB}{W} \times 100 = \frac{2.5}{25} \times 100 = 10%
   \]

Hence, the closest value for the percentage of land lost is approximately **10.45%**.

### Conclusion:
The correct answer is:
**25.00 and 10.45**

Would you like more details or have any questions?

#### Related Questions:
1. How would the results change if the slope of the land increased to 15%?
2. What is the formula for calculating the working width for any given slope and vertical spacing?
3. How do you calculate the total number of terraces needed for a specific length of land?
4. What effect does reducing the vertical spacing have on the percentage of land area lost?
5. How does the batter slope influence the working width and area lost?

#### Tip:
When calculating working widths and land areas for terraces, always account for both the natural slope of the land and the batter slope of the terraces to get accurate results.

It is planned to create bench terraces on land with a 10% slope. With a vertical spacing of 2.5 meters between the terraces and a batter slope of 100%, determine both the working width (in meters) and the percentage of land area lost for cultivation.

Learn how to calculate the working width and percentage of land area lost for bench terraces on land with a 10% slope. Using the Pythagorean theorem and slope geometry, find out how to determine terrace spacing and land usage. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation