How much is the area of a circle with a diameter of 5cm than a circle with a diameter of 2 cm?

The ratio of areas is the square of the ratio of the sides.

Ratio of sides is 5:2, so ratio of areas is 52:22 = 25:4

So the larger circle has an area that is 25/4 = 61/4 (= 6.25) times the area of the smaller circle.

The difference in areas is given by taking the area of the smaller circle from the area of the larger circle.

area_circle = π x radius2

radius = diameter/2

larger_area = π x (5/2)2 cm2

smaller_area = π x (2/2)2 cm2

⇒ difference = larger_area - smaller_area

= (π x 25/4 - π) cm2

= 21π/4 cm2

≈ 16.49 cm2