If two circles have radii of 3 cm and 5 cm, what is the ratio of their areas?

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Question: If two circles have radii of 3 cm and 5 cm, what is the ratio of their areas?

Options:

Correct Answer: 9:25

Solution:

The area of a circle is A = πr². The areas are 9π cm² and 25π cm², so the ratio of their areas is 9:25.

If two circles have radii of 3 cm and 5 cm, what is the ratio of their areas?

If two circles have radii of 3 cm and 5 cm, what is the ratio of their areas?

Step 1: Understand that the area of a circle is calculated using the formula A = πr², where r is the radius.
Step 2: Identify the radii of the two circles. The first circle has a radius of 3 cm, and the second circle has a radius of 5 cm.
Step 3: Calculate the area of the first circle using the formula. A1 = π(3 cm)² = π(9 cm²) = 9π cm².
Step 4: Calculate the area of the second circle using the formula. A2 = π(5 cm)² = π(25 cm²) = 25π cm².
Step 5: Write down the areas of both circles: the first circle is 9π cm² and the second circle is 25π cm².
Step 6: To find the ratio of their areas, compare the two areas: Ratio = Area of first circle : Area of second circle = 9π : 25π.
Step 7: Simplify the ratio by canceling out π: The ratio of their areas is 9 : 25.

Area of a Circle – Understanding the formula A = πr² to calculate the area based on the radius.
Ratio Comparison – Finding the ratio of two quantities, in this case, the areas of two circles.