The circumference of a circle exceeds its diameter by 180 cm. Calculate :

(i) the radius

(ii) the circumference and

(iii) the area of the circle.

(i) Given,

Circumference of a circle exceeds diameter by 180 cm.

So, Circumference = Diameter + 180

Circumference - Diameter = 180

$\Rightarrow 2\pi r - 2r = 180 \\[1em] \Rightarrow 2r(\pi - 1) = 180 \\[1em] \Rightarrow 2r\Big(\dfrac{22}{7} - 1\Big) = 180 \\[1em] \Rightarrow 2r\Big(\dfrac{22 - 7}{7}\Big) = 180 \\[1em] \Rightarrow 2r\Big(\dfrac{15}{7}\Big) = 180 \\[1em] \Rightarrow 30r = 180 × 7 \\[1em] \Rightarrow 30r = 1260 \\[1em] \Rightarrow r = \dfrac{1260}{30} \\[1em] \Rightarrow r = 42 \text{ cm}.$

Hence, radius = 42 cm.

(ii) As calculated,

Radius = 42 cm.

Circumference of circle = 2πr

= 2 × $\dfrac{22}{7}$ × 42

= 2 × 22 × 6

= 44 × 6 = 264 cm.

Hence, circumference of circle = 264 cm.

(iii) By formula,

Area of circle = πr²

= $\dfrac{22}{7}$ × (42)²

= $\dfrac{22}{7}$ × 1764

= 22 × 252

= 5544 cm².

Hence, area of circle = 5544 cm².