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

Answer:

25 : 1

Step-by-step explanation:

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.

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 is:

A : a

$100\pi r^2 : 4\pi r^2$

= 100 : 4

25 : 1

Answer 2

Ratio of the surface area of football and cricket ball = 25 : 1

Recall:

• Surface area of a sphere = 4πr², where, r = radius of the sphere

Given:

• Diameter of football = 5 times diameter of cricket ball

By implication,

radius of football = 5 times radius of cricket ball

Let,

• R = radius of football
• r = radius of cricket ball
• A = Surface area of football
• a = Surface area of cricket

This means that:

R = 5r

Surface Area of Football:

A = 4 × π × (5r)²

A = 100πr²

Surface Area of Cricket ball:

a = 4 ×π × (r)²

a = 4πr²

Ratio of surface area of football and cricket ball = 100πr² : 4πr² = 25 : 1

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