A circular carpet of 1.4 m is spotted in the centre with 20 cm striped border. Find the area of striped border to the nearest cm²
First, we find the area of the whole carpet, including the striped border. Since the carpet is circular with a diameter of 1.4 m, the radius is 1.4/2 = 0.7 m. The area of the entire carpet is given by the formula for the area of a circle, which is A = πr², where A is the area, and r is the radius:
A = π(0.7)² = π(0.49)
Now we find the area of the circle without the striped border. The radius of this circle is the total radius (0.7 m) minus the width of the striped border (20 cm or 0.2 m):
New radius = 0.7 - 0.2 = 0.5 m
The area of this inner circle is given by the same formula:
A' = π(0.5)² = π(0.25)
Now, to find the area of the striped border, we simply subtract the area of the inner circle from the area of the entire carpet:
Area of the striped border = π(0.49) - π(0.25)
Factor out the π:
Area of the striped border = π(0.49 - 0.25) = π(0.24)
Now, we can evaluate the area of the striped border numerical value.
Area of the striped border ≈ 3.14 * 0.24 ≈ 0.7536 square meters
Since 1 square meter is equal to 10,000 square centimeters, the area of the striped border is:
0.7536 * 10,000 ≈ 7536 square centimeters
So, the area of the striped border is approximately 7536 cm².