four equal circles are described at the four corners of a square so that each circle touches two of the others find the area of the space enclosed between the circumference of the circles each side of the square measuring 24 cm
Answers
Answer:
Answer
The side of Square is given by 24cm
Area of Square is a
2
=24
2
=576cm
2
The Radius of the 4 circles at corners of square is given by
2
24
=12
The Area of quadrant of circle in side the Square is
4
1
×π×r
2
Since there are 4 such quadrants ⟹4×
4
1
πr
2
=πr
2
⟹π(12)(12)=144π=3.14(144)=452.16
So the area of remaining portion is 576−452.16=123.84
Answer:
123.84 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
= 113.04 cm²
Area of 4 such circles = 4*113.04
= 452.16 cm²
∴ Area enclosed between the circumference of the circles and square =
⇒ area of square - area of 4 circles
⇒ side² - 452.16
⇒ 24² - 452.16
⇒ 123.84 cm²
(Area enclosed in circumference of circle = area of circle
= 4*113.04 = 452.16 cm²)