The circumference of a circle is 123.2 cm. Calculate :

(i) the radius of the circle in cm.

(ii) the area of the circle in cm², correct to nearest cm².

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

(i) Let radius = r cm.

By formula,

Circumference = 2πr

2πr = 123.2

$\Rightarrow 2 \times \dfrac{22}{7} \times r = 123.2 \\[1em] \Rightarrow r = \dfrac{123.2 \times 7}{22 \times 2} \\[1em] \Rightarrow r = \dfrac{862.4}{44} = 19.6 \text{ cm}$

Hence, radius = 19.6 cm.

(ii) By formula,

Area of circle = πr²

$= \dfrac{22}{7} \times (19.6)^2 \\[1em] = \dfrac{22}{7} \times 384.16 \\[1em] = 22 \times 54.88 \\[1em] = 1207.36 ≈ 1207 \text{ cm}^2.$

Hence, area of circle = 1207 cm².

(iii) We know that,

Area of circle = πr², where r is the radius.

If radius is doubled so new radius = 2r cm.

New area of circle = π(2r)² = 4πr².

Change in area = $\dfrac{\text{New area}}{\text{Area of circle}} = \dfrac{4πr^2}{πr^2} = 4$

Hence, area becomes 4 times.