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).