The difference between circumference and diameter of a circle is 135cm. Find the radius of the circle. Take π = 22/7.

The relationship between the circumference (C) and diameter (D) of a circle can be expressed with the formula:

Key Formulas

• C = π × D
• D = 2 × r (where r is the radius)

According to the problem, the difference between the circumference and diameter is 135 cm:

C - D = 135 cm

Substituting the Formula

Using the first formula, we can rewrite the equation:

π × D - D = 135 cm

Factoring out D gives:

D(π - 1) = 135 cm

Calculating Diameter

Now, substituting π with 22/7:

D(22/7 - 1) = 135 cm

First, convert 1 to a fraction:

D(22/7 - 7/7) = 135 cm

This simplifies to:

D(15/7) = 135 cm

To find D, multiply both sides by the reciprocal of 15/7:

D = 135 cm × (7/15)

Calculating this gives:

D = 63 cm

Finding the Radius

Now, use the diameter to find the radius:

r = D/2 = 63 cm / 2 = 31.5 cm

Final Answer

The radius of the circle is 31.5 cm.