Question

If one circle has a diameter of 20 cm and a second circle has a diameter of 40 cm, what is the ratio of the area of the larger circle to the area of the smaller circle?

Answer 1

The ratio of the area of the larger circle to the area of the smaller circle will be: 4/1 or 4:1

Explanation:

The diameter of a larger circle = d = 40 cm

r = d/2 = 40/2 = 20 cm

The area of the larger circle = πr²

= 3.14 (20)²

= 3.14 × 400

= 1256 cm²

The diameter of a smaller circle = 20 cm

r = d/2 = 20/2 = 10 cm

The area of the smaller circle = πr²

= 3.14 (10)²

= 3.14 × 100

= 314 cm²

Thus,

The area of the larger circle = 1256 cm²

The area of the smaller circle = 314 cm²

Therefore,

The ratio of the area of the larger circle to the area of the smaller circle will be computed as:

• 1256:314 or 1256/314

reducing the ration into a simpler form

• 1256/314 = 4/1

Thus, the ratio of the area of the larger circle to the area of the smaller circle will be: 4/1 or 4:1