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Question:

If the difference between the circumference and the radius of a circle is 37cm, then using π=22/7, the circumference (in cm) of the circle is:

154

7

44

14

Solution:

Let the radius of circle be r
Then circumference of circle = 2πr
Then, the difference between the circumference and circle = 2πr - r
But given that the difference between the circumference and circle = 37cm
∴ 2πr - r = 37 → r(2π - 1) = 37 → r = 37/(2π - 1) cm
→ r = 37/(2 × 22/7 - 1) cm
→ r = 37 × 7/(44 - 7) cm
→ r = 37 × 7/37 = 7 cm
Then, circumference of circle = 2π × 7 = 2 × 22/7 × 7 = 44 cm