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?

• A. 4 times
• B. 8 times
• C. 16 times
• D. 82 times

Answer: (C)

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)

The π canc