A family decides to build a circular pathway around the pool. The pool has a radius of 4 m and the walkway will extend 2 m around the pool if each square meter of tile cost $15. What is the cost of the walkway?
First, we calculate the area of the pool:
Area of pool = π × radius^2
Area of pool = π × 4^2
Area of pool = π × 16
Area of pool = 50.24 m^2
Next, we calculate the area of the pool plus the walkway:
Area of pool + walkway = Area of pool + (2 × width of walkway) × (2 × radius + width of walkway)
Area of pool + walkway = 50.24 + (2 × 2) × (2 × 4 + 2)
Area of pool + walkway = 50.24 + 4 × 10
Area of pool + walkway = 50.24 + 40
Area of pool + walkway = 90.24 m^2
Finally, we calculate the cost of the walkway:
Cost of walkway = Area of walkway × cost per square meter
Cost of walkway = 90.24 × 15
Cost of walkway = $1353.60
Therefore, the cost of the walkway around the pool is $1353.60.