Question

Four equal circles are described about the four corners of a square so that each circle touches two of the others Find the area of the space enclosed between the circumstances of the circles,each side of the square measuring 24cm​

Answer 1

Answer:

123.43 cm²

Step-by-step explanation:

Note that: sum of diameters of 2 circles is equal to the length of the side of square.   Let the radii of the circles be r.

⇒ (diameter) + (diameter) = 24cm

⇒ (2r) + (2r) = 24 cm

⇒ r = 6 cm

Thus,

area of 1 circle = πr² = (22/7) 6²

                        = 113.14 cm²

Area of 4 such circles = 4*113.14

                         = 452.57 cm²

If it is about the area enclosed between the circumference and square:

Area enclosed between the circumference  of the circles and square =

⇒ area of square - area of 4 circles

⇒ side² - 452.57

⇒ 24² - 452.57

⇒ 123.43 cm²

Answer 2

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Four equal circles are described about the four corners of a square so that each circle touches two of the others Find the area of the space enclosed between the circumstances of the circles,each side of the square measuring 24cm.

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• Side of the square = 24 cm

• Radius of the circle = $\sf{\dfrac{24}{2}}$
• ㅤㅤ"ㅤ "ㅤ"ㅤㅤ" ㅤ = 12 cm

•°• Area of the quadrant of one circle

ㅤㅤㅤㅤㅤㅤ= $\sf{\dfrac{1}{4} π r²}$

ㅤㅤㅤㅤㅤㅤ= $\sf{\dfrac{1}{4} \times \dfrac{22}{7} \times 12 \times 12}$

ㅤㅤㅤㅤㅤㅤ= $\sf{\dfrac{792}{7}}$

ㅤㅤㅤㅤㅤㅤ= $\sf{113.14}$ cm²

• Area of the quadrants of four circles

ㅤㅤㅤㅤㅤㅤ= 113.14 × 4

ㅤㅤㅤㅤㅤㅤ= 452.56 cm²

• Now , Area of square = ( s )²

ㅤㅤㅤㅤㅤㅤ= ( 24 )²

ㅤㅤㅤㅤㅤㅤ= 576 cm²

Now , $\sf{Area_{(Square)} \:-\: Area_{(Quadrant\:of\:circles)}}$

• = ( 576 - 452.56 ) cm²

• = 123.44 cm²ㅤㅤㅤAns...

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