Four equal circles are described at the four corners of a square so that each touches two of the others. The shaded area enclosed between the circles is 24/7cm2. Find the radius of each circle.
Answers
Answered by
317
Shaded area = area of square - sum of areas of 4 quadrants
Let the radius of circle be r cm
then side of square will be 2r cm
A/q
24/7 = (2r)² - 4×(1/4)×πr²
=4r² - 22/7 r²
⇒24/7 = 6r²/7
⇒r² =4
⇒r =2 cm
hence , the radius of each circle is 2 cm
Let the radius of circle be r cm
then side of square will be 2r cm
A/q
24/7 = (2r)² - 4×(1/4)×πr²
=4r² - 22/7 r²
⇒24/7 = 6r²/7
⇒r² =4
⇒r =2 cm
hence , the radius of each circle is 2 cm
Answered by
68
Answer:
Step-by-step explanation:
r = a/2)
24/7 = a² - 4(1/4 x π x r² )
24/7 = a² - π x(a/2)²
24/7 = a² - π x a² / 4
24/7 = a² - 22/7 x a² /4
24/7 = a² - 11a² / 14
24/7 =(14a² - 11a²)/14
24 = 3a² / 2
a² = 24 x 2 / 3
a² = 16
a = √16
a = 4 cm.
r = a/2
= 4/2
r = 2 cm..... Therefore the radius of each circle is 2 cm
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