Question

The diameter of a football is five times the diameter of a cricket ball.Ratio of surface area of football and cricket ball is .......

Answer 1

hello there!!!

let D and d be the diameter of football and cricket ball respectively

now radius of football,R=D÷2
now radius of cricket ball ,r=d÷2
Now, D = 5d =>2R=10r =>R = 5r
now surface area of football ×surface area of cricket ball = 4πR²4πr² = (Rr)² = (5rr)²= 25/1

Answer 2

Answer:

The ratio of the surface area of football and cricket balls will be 25:1.

Step-by-step explanation:

Given: The diameter of a football is five times the diameter of a cricket ball.

We have to find the ratio of the surface area of football and cricket ball.

We are solving in the following way:

We have,

The diameter of the football is 5 times the diameter of the cricket ball.

This means that the radius of the football is also 5 times the radius of the cricket ball.

Let the radius of the football be R.

Let the radius of the cricket ball be r.

This implies that:

$R=5r$

Both balls are spherical.

Therefore the surface area of the cricket ball is given as:

$a = 4\pi r^2$

The surface area of the football is given as:

$A = 4\pi R^2\\=>A = 4\pi (5r)^2\\=> A = 100\pi r^2$

Therefore, the ratio of their surface areas will be:

A:a

$100\pi r^2 : 4\pi r^2\\= 100 : 4\\=25 : 1$

Hence, the ratio of the surface area of football and cricket balls will be 25:1.