Question 1
Q1A circular garden with a radius of 10 meters is to be surrounded by a walkway. The area of the walkway is 75% of the area of the garden. What is the approximate width of the walkway?
graph TD
subgraph Garden and Walkway
A((Garden
Radius = 10m)) -->|Width = x| B((Walkway))
end
style A fill:#9f9,stroke:#333,stroke-width:2px
style B fill:#ccc,stroke:#333,stroke-width:2px
Show answer & explanation
Correct answer: B
- Area of the garden (Ag) = π * r^2 = π * (10)^2 = 100π square meters.
- Area of the walkway (Aw) is 75% of the garden's area: Aw = 0.75 * 100π = 75π square meters.
- The total area of the garden plus walkway (At) is Ag + Aw = 100π + 75π = 175π.
- Let R be the radius of the entire circle (garden + walkway). At = π * R^2. So, 175π = π * R^2, which means R^2 = 175. R = √175 ≈ 13.23 meters.
- The width of the walkway is the difference between the total radius and the garden's radius: Width = R - r = 13.23 - 10 = 3.23 meters. The closest answer is 3.2 meters.
