The circumference of a circle is 123.2 cm. Calculate :

(i) the radius of the circle in cm;

(ii) the area of the circle to the nearest cm²;

(iii) the effect on the area of the circle if the radius is doubled.

Let the radius of circle be r cm.

(i) Circumference of circle = 2πr

⇒ 123.2 = 2 × $\dfrac{22}{7}$ × r

⇒ r = $\dfrac{123.2 × 7}{2 × 22}$

⇒ r = $\dfrac{862.4}{44}$ = 19.6 cm.

Hence, radius of circle = 19.6 cm.

(ii) Area of circle = πr²

= $\dfrac{22}{7}$ × (19.6)²

= $\dfrac{22}{7}$ × 19.6 × 19.6

= 22 × 2.8 × 19.6

= 1207.36

≈ 1207 cm².

Hence, area of circle = 1207 cm².

(iii) Area of circle = π(radius)²

If radius is double then it will become 2r.

New area = π(2r)²

= π × 4r²

= 4 × πr².

Hence, new area becomes 4 times the old area.