Question

The difference of radii of two circles is 3 cm and the sum of their circumferences is 44 cm. Calculate the radii of the circles.

Answer 1

Given:

• The difference of the radii of two circles is 3 cm.
• The sum of their circumferences is 44 cm.

Stepwise calculation:

1. Let the radii of the two circles be R and r, where R > r.

2. From the difference of the radii: R – r = 3   ...(i)

3. Sum of the circumferences of the two circles is 44 cm:

2πR + 2πr = 44

2π(R + r) = 44

Taking `π = 22/7`

`2 xx 22/7 (R + r) = 44`

⇒ `(R + r) = (44 xx 7)/(2 xx 22) = 7`   ...(ii)

4. Adding equation (i) and (ii):

(R – r) + (R + r) = 3 + 7

2R = 10

⇒ R = 5 cm

5. Substituting R = 5 in equation (ii) gives:

5 + r = 7

⇒ r = 2 cm

The radius of the larger circle is 5 cm.

The radius of the smaller circle is 2 cm.