Question

Calculate the area of the shaded region in the given figure, common between the two quadrants of the circles of radius 10 cm each.
(use $\pi$ = 3.14)

• A. 60 ${cm}^2$
• B. 57 ${cm}^2$
• C. 58 ${cm}^2$
• D. 67 ${cm}^2$

Answer 1

The correct option is B 57 ${cm}^2$

Let us divide the figure as shown below:

Area of Sector = $\pi$$r^2$$\times$$\frac{x^{\circ }}{{360}^{\circ }}$

Given, radius = 10 $cm$ and sector ADOB is making angle ${90}^{\circ }$ with the centre.
so,
Area of sector ADOB = $\pi$${\left(10\right)}^2$$\times$$\frac{90}{360}$
= 78.5 ${cm}^2$
Area of $△$ADB = $\frac{1}{2}$$\times$(AD)$\times$(AB)
= $\frac{1}{2}$$\times$(10)$\times$(10)
= 50 ${cm}^2$
Area of segment DBO = [Area of segment ADOB - Area of $△$ADB]
=[78.5 - 50] ${cm}^2$
So, Area of segment DBO = 28.5 ${cm}^2$

Now, Area of required shaded region
= 2$\times$Area of segment DBO
= 2$\times$28.5 ${cm}^2$ = 57 ${cm}^2$
Hence, Area of required shaded region = 57 ${cm}^2$