A traffic roundabout has a circular garden
in the centre and two lanes for traffic encircling the garden. The diameter of the garden is 16 metres and each lane is 3 metres wide. Each lane is to be resurfaced. Calculate the area to be resurfaced. Answer in square metres to the nearest whole number.

To calculate the area that needs to be resurfaced, we need to find the area of the two traffic lanes around the circular garden.

### Steps:

1. **Garden's Diameter and Radius:**
   - Diameter of the garden = 16 meters
   - Radius of the garden \( r_1 \) = \( \frac{16}{2} = 8 \) meters

2. **Total Diameter Including Both Lanes:**
   - Each lane is 3 meters wide, so the total width added by the two lanes is \( 2 \times 3 = 6 \) meters.
   - Total diameter of the roundabout = \( 16 + 6 = 22 \) meters
   - Total radius of the roundabout \( r_2 \) = \( \frac{22}{2} = 11 \) meters

3. **Area of the Whole Roundabout:**
   The area of a circle is given by the formula:
   \[
   A = \pi r^2
   \]
   The area of the entire roundabout (including the garden and the lanes) is:
   \[
   A_{\text{whole}} = \pi \times 11^2 = 121\pi \text{ square meters}
   \]

4. **Area of the Garden:**
   The area of the garden (central circle) is:
   \[
   A_{\text{garden}} = \pi \times 8^2 = 64\pi \text{ square meters}
   \]

5. **Area to be Resurfaced:**
   The area to be resurfaced is the area of the two lanes, which is the difference between the total roundabout area and the garden area:
   \[
   A_{\text{resurface}} = A_{\text{whole}} - A_{\text{garden}} = 121\pi - 64\pi = 57\pi
   \]
   \[
   A_{\text{resurface}} = 57 \times 3.1416 = 179.07 \text{ square meters}
   \]
   
   Rounding to the nearest whole number, the area to be resurfaced is **179 square metres**.

### Final Answer:
The area to be resurfaced is **179 square metres**.

Would you like any more details or have questions? Here are 5 related questions:

1. How do you calculate the area of a circular shape?
2. What is the significance of π in these calculations?
3. How does the width of lanes affect the total surface area to be resurfaced?
4. Can you explain how to convert between radius and diameter?
5. How would the area change if the lanes were wider?

**Tip:** Always ensure you are subtracting the correct areas when calculating for annular regions (like in roundabouts).

A traffic roundabout has a circular garden in the centre and two lanes for traffic encircling the garden. The diameter of the garden is 16 metres and each lane is 3 metres wide. Each lane is to be resurfaced. Calculate the area to be resurfaced. Answer in square metres to the nearest whole number.

Learn how to calculate the area to be resurfaced for a traffic roundabout with a circular garden in the center. This problem involves geometric concepts like the area of circles and annular regions, using the formula A = πr^2. The lanes are 3 metres wide, and the total area to be resurfaced is 179 square metres.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation