Why are the areas of unshaded regions in the two figures equal?

The radius of the quarter circles in figure 1 is equal to the radius of the circle in figure 2

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The radii of the quarter circles are equal.

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Both A and B

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None of the above

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Solution

The correct option is C Both A and B
The two areas are equal because the four quarter circles in the first figure have the same radius as the circle. The area of shaded region in the first figure is the area of the square without the four quarter circles (marked as 1,2,3 and 4), and the area of the shaded region in the second figure is the area of the square without the circle. Also, the radii of the quarter circles 1,2,3 and 4 are equal.

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Similar questions

The areas of the shaded regions in figures 1 and 2 are equal. The corresponding lengths and breadths of both the rectangles are equal, and the radius of the quarter circles in figure 1 is half the breadth of the rectangle.

Areas of the shaded regions in figures 1 and 2 are equal.

[The corresponding lengths and breadths of the rectangles are equal, and the radius of the quarter circles in figure 1 is half the breadth of the rectangle.]

State true or False.
Areas of the shaded regions in figures 1 and 2 are equal. The corresponding lengths and breadths of the rectangles are equal, and the radius of the quarter circles in figure 1 is half the breadth of the rectangle.

Why are the areas of unshaded regions in the two figures equal?

P Q R S

is the diameter of a circle of radius

6 c m

. The length

P Q, Q R

and

R S

are equal. Semi-circle is drawn with

P Q

and

Q S

as diameters as shown in the figure. The ratio of the area of the shaded region to that of the unshaded region is

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