A circular lake 30 meters in diameter is surrounded by a tile path 5 meters wide. Find the area of the tile path. Round to the nearest tenth.
What is
π(20)^2 - π(15)^2 ?
To find the area of the tile path, we need to subtract the area of the inner circle from the area of the outer circle.
Step 1: Find the radius of the inner circle.
The diameter of the inner circle is given as 30 meters. The radius can be calculated by dividing the diameter by 2.
Radius of the inner circle = 30 meters / 2 = 15 meters
Step 2: Calculate the area of the inner circle.
The area of a circle is given by the formula: A = π * r^2, where A is the area and r is the radius.
Area of the inner circle = π * (15 meters)^2 = 706.9 square meters (rounded to the nearest tenth)
Step 3: Find the radius of the outer circle.
The diameter of the outer circle is the sum of the diameter of the inner circle and the width of the tile path on both sides, which is 5 meters.
Diameter of the outer circle = 30 meters + 5 meters + 5 meters = 40 meters
Radius of the outer circle = 40 meters / 2 = 20 meters
Step 4: Calculate the area of the outer circle.
Area of the outer circle = π * (20 meters)^2 = 1256.6 square meters (rounded to the nearest tenth)
Step 5: Calculate the area of the tile path.
Area of the tile path = Area of the outer circle - Area of the inner circle = 1256.6 square meters - 706.9 square meters = 549.7 square meters (rounded to the nearest tenth)
Therefore, the area of the tile path is approximately 549.7 square meters.