Approximately how many times greater is the area of a circle with a diameter of 200 mm compared to that of a circle with a diameter of 40 mm?

To understand why the area of the larger circle is approximately 16 times greater than that of the smaller circle, we start with the formula for the area of a circle, which is A = πr², where r is the radius of the circle.

First, let's calculate the area of the circle with a diameter of 200 mm. The radius would be half of the diameter, so the radius is 100 mm.

Area of the larger circle:

A₁ = π(100 mm)²

A₁ = π(10,000 mm²)

A₁ = 10,000π mm²

Next, we calculate the area of the smaller circle with a diameter of 40 mm. The radius is half of 40 mm, so it is 20 mm.

Area of the smaller circle:

A₂ = π(20 mm)²

A₂ = π(400 mm²)

A₂ = 400π mm²

Now, to find how many times greater the area of the larger circle is compared to the smaller one, we take the ratio of their areas:

Ratio = A₁ / A₂ = (10,000π mm²) / (400π mm²)

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