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 ? Show your work.

Answer 1

Assume the radius of the circle as r cm and write the equation for the area as:

300/360 × πr² = 120π

=> 5/6 × r² = 120

=> r² = (120 × 6)/5

=> r² = 144

=> r = 12 cm

Finds the length of ribbon required as:

r + r + θ/360 × 2πr

=> 2r + 300/360 × 2π × 12

=> 2 × 12 + 20π

=> (24 + 20π) cm