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Q.

Find the area of the unshaded region in the figure, where PQRS is a square of 30 cm.

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a

(900−225π)cm2

b

(800−325π)cm2

c

(700−225π)cm2

d

(900−285π)cm2

answer is A.

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Detailed Solution

Area of square PQRS=(30)2 cm2= 900 cm2
We were also given four circles in the square PQRS. Let us assume the diameter of a circle is equal to “d”.
The sum of the diameters of two circles is equal to the side of the square.
⇒2d = 30cm
⇒d = 15cm
Area of unshaded region= Area of the square – Area of four circles in the square.
So, the area of circle =

\frac{π d^{2}}{4} .

= \frac{π {(15)}^{2}}{4} = \frac{225 π}{4}

Area of four circles

= 4 (\frac{225 π}{4}) = 225 π

Area of unshaded region = Area of square PQRS – Area of four circles of diameter 15 cm
Area of unshaded region

= (900 - 225 π) c m^{2}

Hence, the area of unshaded region in the square PQRS is

(900 - 225 π) c m^{2} .

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