Question

Wasim made a model of Pac-Man, after playing the famous video game of the same name. The area of the model is 120π cm². Pac-Man's mouth forms an angle of 60° at the centre of the circle. 

A picture of the model is shown below.

Wasim wants to decorate the model by attaching a coloured ribbon to the entire boundary of the shape. What is the minimum length of the ribbon required in terms of ?

Answer 1

Assumes the radius of the circle as r cm and writes the equation for the area as:

120π = 300/360 × π × r²

⇒ r = 12 cm

Finds the length of ribbon required as:

(300/360 × 2 × π × 12) + 24 cm = (20π + 24) cm