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Q.

The difference between the area and square of radius of a circle is 105 cm. What will be the circumference of the circle?

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a

44 cm

b

42 cm

c

40 cm

d

38 cm 

answer is A.

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Detailed Solution

Given that, the difference lies between the area of a circle and the square of its radius is 105 centimeters.
Let r represents the radius of the circle.
Make an equation with the help of difference lies between the area of a circle A and the square of its radius r2 .
A− r 2 =105    Substitute π r 2   for A into the equation.
π r 2 − r 2 =105   Taking out r2 from left side of the equation,
r 2 p−1 =105   Substitute 3.14  for π   into the equation.
r 2 2.14 =105   Divide by 2.14  on both sides of the equation.
r 2 = 105 2.14   ⇒ 49
Solving the equation for r,
r = 7
Determining the circumference by substituting 7 for r into the equation C=2pr  ,  C=2× 22 7 ×7   ⇒C= 44cm
Therefore, circumference related to the circle is 44 cm.
Hence the correct option is 1.
 
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