Question

If the 200 cm side Square and a quarter of radius 28 cm are cut from four sides. What is the remaining area?

Answer 1

Correct Answer: 37539.84

To find the remaining area after cutting four quarters of a circle (each with a radius of 28 cm) from a square with a side length of 200 cm, follow these steps:
1. Calculate the area of the square:
\[\text{Area of the square} = \text{side}^2 = 200^2 = 40000 \, \text{cm}^2\]
2. Calculate the area of one quarter circle:
The radius of each quarter circle is 28 cm.
\[\text{Area of one quarter circle} = \frac{1}{4} \times \pi \times \text{radius}^2 = \frac{1}{4} \times \pi \times 28^2 = \frac{1}{4} \times \pi \times 784 = 196 \pi \, \text{cm}^2\]
3. Calculate the total area of the four quarter circles:
Since there are four quarters, their total area is:
\[\text{Total area of four quarters} = 4 \times 196 \pi = 784 \pi \, \text{cm}^2\]
4. Calculate the remaining area after cutting out the quarter circles:
Subtract the total area of the four quarter circles from the area of the square:
\[\text{Remaining area} = 40000 - 784 \pi \, \text{cm}^2\]
5. Approximate the remaining area:
Using \(\pi \approx 3.14\),
\[784 \pi \approx 784 \times 3.14 = 2460.16 \, \text{cm}^2\]
So, the remaining area is approximately:
\[\text{Remaining area} \approx 40000 - 2460.16 = 37539.84 \, \text{cm}^2\]
Therefore, the remaining area after cutting out the quarters of a circle is approximately \(37539.84 \, \text{cm}^2\).