To determine the length of the outer curve where a railing has to be put, let's walk through the necessary steps.
1. Understand the Road Dimensions:
- The road is 20 feet wide.
- There are two curves: an inner curve and an outer curve. The outer curve is created by extending the inner curve outwards by the width of the road.
2. Define the Given Parameters:
- Road width, [tex]\( W = 20 \)[/tex] feet.
- Assume that the radius of the inner curve is [tex]\( r \)[/tex].
3. Calculate the Radius of the Outer Curve:
- The radius of the outer curve would be the radius of the inner curve plus the width of the road.
- Thus, if the radius of the inner curve is [tex]\( r \)[/tex]:
[tex]\[
\text{Radius of the outer curve } = r + 20 \text{ feet}
\][/tex]
4. Find the Length of the Outer Curve:
- The formula for the circumference (length of the curve) of a circle is given by [tex]\( C = 2\pi \cdot \text{radius} \)[/tex].
- Therefore, for our outer curve:
[tex]\[
\text{Length of the outer curve} = 2\pi \cdot (r + 20)
\][/tex]
5. Simplify the Formula with Given Values:
- We do not have the exact value of [tex]\( r \)[/tex], but let's focus on the outer radius and length calculation.
- Using [tex]\(\pi = 3.14\)[/tex]:
[tex]\[
\text{Length of the outer curve} = 2 \cdot 3.14 \cdot 20
\][/tex]
6. Calculate the Outer Curve Length:
- Substituting the values into the formula:
[tex]\[
\text{Length of the outer curve} = 2 \cdot 3.14 \cdot 20 = 125.6 \text{ feet}
\][/tex]
7. Round to the Nearest Foot:
- The length of the outer curve, 125.6 feet, rounded to the nearest foot is 126 feet.
Therefore, the length of the outer curve is 126 feet.
