Question

The diameter of a football is five times the diameter of a cricket ball then what is the ratio of surface areas of football and cricket ball?

Answer 1

This is a question that deals with scale factors, there are three scale factors

i) Linear scale factor
ii) Area scale factor
iii) Volume scale factor

Area scale factor = (Linear scale factor)²
Volume scale factor = (Linear scale factor)³


In this question, linear scale factor = Diameter of football/Diameter of cricket ball = 5/1 (Five times)

Area scale factor is therefore (5/1)² = 25/1

This means the ratio of the surface areas of football and cricket ball = 25:1

Answer 2

Solution :-

Given that the diameter of a football is five time the diameter of a cricket ball.

The ratio of the diameter of football to the diameter of cricket ball = 5 : 1

Then, the ratio of radius of football to the radius of cricket ball will also be 5 : 1

Then, the ratio of surface area of football to the surface area of cricket

= (5)² : (1)²

⇒ 25 : 1

So, the ratio of surface area of football to the surface area of cricket ball is 25 : 1

Answer.