From a rectangular cardboard sheet of length 46 m and breadth 8 m, three circular plates of radii 3 m, 2 m and 1 m are cut out. If the area of the remaining part of the cardboard sheet is equal to the area of a square, then find the length of each side of the square (use π = 22/7).
18 m
Here's how to solve this problem step-by-step:
1. Calculate the area of the rectangular cardboard sheet:
Area of rectangle = length × breadth = 46 m × 8 m = 368 \(m^2\)
2. Calculate the area of each circular plate:
- Area of circle 1 (radius 3 m) = π × \(3^2\) = \( \frac{22}{7} \times 9 = \frac{198}{7} m^2\)
- Area of circle 2 (radius 2 m) = π × \(2^2\) = \( \frac{22}{7} \times 4 = \frac{88}{7} m^2\)
- Area of circle 3 (radius 1 m) = π × \(1^2\) = \( \frac{22}{7} \times 1 = \frac{22}{7} m^2\)
3. Calculate the total area of the three circular plates:
Total area = \(\frac{198}{7} + \frac{88}{7} + \frac{22}{7} = \frac{308}{7} = 44 m^2\)
4. Calculate the area of the remaining part of the cardboard sheet:
Remaining area = Area of rectangle - Total area of circles = 368 \(m^2\) - 44 \(m^2\) = 324 \(m^2\)
5. Find the side length of the square with the same area as the remaining part of the cardboard:
Area of square = side × side = \(side^2\) = 324 \(m^2\)
Side = \(\sqrt{324}\) = 18 m
Therefore, the length of each side of the square is 18 m.
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