From each corner of a square of side a quadrant of a circle of radius a quadrant of a circle of radius is cut and also a circle of diameter is cut and also a circle of diameter is cut as shown in figure. Find the area of the remaining portion of the square.

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\frac{68}{7} {cm}^{2}

\frac{88}{7} {cm}^{2}

\frac{78}{7} {cm}^{2}

\frac{68}{8} {cm}^{2}

answer is A.

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Detailed Solution

Concept- Determine the area of the square. Then compute the area of all the square pieces that are clipped away. Subtract the area of the chopped section from the area of the square. The remaining region will be the solution.
Question Image

It is given in the question that

is a square with side, say,

A quadrant of radius, say,

is cut from all four corners of the square.
A quadrant is the fourth section of a circle, as we can see. That is, four quadrants will join to make one circle. As a result, the area cut by four quadrants equals the area cut by one circle.
A circle with a diameter of 2 cm is also carved from the middle. However, the diameter is double the radius. That is, a 1 cm radius circle is carved from the center.
However, the quadrants have a radius of one as well. This means that the radius of the circle generated by combining the four quadrants and the radius of the circle formed by cutting from the center are equal.
To tackle this issue, we employ the ideas of area of rectangles and area of sectors of circles.
The circle that is carved out has a diameter of 2 cm. This circle's radius is 1 cm.
Radius of all sliced quadrants (r) equals 1 cm
Area of parts taken out of the square equals Area of the circle plus four since all of the quadrants have the same radius (Area of each quadrant) .

Area of the square minus the area of the piece that was taken away equals the area of the remaining square.

Hence, the correct option is 1.

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