If two circles have radii of 4 cm and 6 cm, what is the ratio of their areas?

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Question: If two circles have radii of 4 cm and 6 cm, what is the ratio of their areas?

Options:

Correct Answer: 4:9

Solution:

Area ratio = (r1^2):(r2^2) = (4^2):(6^2) = 16:36 = 4:9.

If two circles have radii of 4 cm and 6 cm, what is the ratio of their areas?

If two circles have radii of 4 cm and 6 cm, what is the ratio of their areas?

Step 1: Identify the radii of the two circles. The first circle has a radius of 4 cm and the second circle has a radius of 6 cm.
Step 2: Recall the formula for the area of a circle, which is Area = π * r^2, where r is the radius.
Step 3: Calculate the area of the first circle using its radius: Area1 = π * (4 cm)^2 = π * 16 cm^2.
Step 4: Calculate the area of the second circle using its radius: Area2 = π * (6 cm)^2 = π * 36 cm^2.
Step 5: To find the ratio of the areas, we compare Area1 to Area2: Area ratio = Area1 : Area2 = (π * 16 cm^2) : (π * 36 cm^2).
Step 6: The π cancels out in the ratio, so we have: Area ratio = 16 : 36.
Step 7: Simplify the ratio 16 : 36 by dividing both numbers by their greatest common divisor, which is 4. This gives us 4 : 9.

Area of a Circle – The area of a circle is calculated using the formula A = πr², where r is the radius.
Ratio of Areas – The ratio of the areas of two circles can be determined by the square of the ratio of their radii.