# On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the squa - Mathematics

Sum

On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.

#### Solution

Let a be the side of square ABCD.

Area of square ABCD =784 cm2

⇒ a^2 = 784

⇒ a = sqrt(784)

= sqrt(2 xx 2 xx 2 xx 2 xx 7 xx 7)

= 2 xx 2 xx 7

⇒ a = 28 cm

Now, in four circles,

4r = AB

⇒ 4r = 28 cm

⇒ r = 7 cm

Area enclosed between circles and square

= Area of square – Area of 4 circles

= 784 - 4pir^2

= 784 - 4 xx 22/7 xx 7 xx 7

= 784 - 616

= 168 cm2.

Hence, the area of square sheet not covered by circular plates is 168 cm2.

Concept: Area of Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.4 | Q 10 | Page 133

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