Calculate Circle Area Ratio: Comparing 4 cm vs 10 cm Diameter Circles

To solve this problem, follow these steps:

• Step 1: Calculate the radius of each circle.
• Step 2: Use the formula for the area of a circle to find the areas.
• Step 3: Find the ratio of the areas to determine how many times larger circle 2's area is compared to circle 1's.

Step 1:
The diameter of circle 1 is 4 cm. Therefore, the radius of circle 1 is $\frac{4}{2} = 2$ cm.

The diameter of circle 2 is 10 cm. Therefore, the radius of circle 2 is $\frac{10}{2} = 5$ cm.

Step 2:
The area of a circle is given by $A = \pi r^2$.
Area of circle 1 is $A_1 = \pi (2)^2 = 4\pi$ square cm.

Area of circle 2 is $A_2 = \pi (5)^2 = 25\pi$ square cm.

Step 3:
To find out how many times larger circle 2's area is than circle 1's area, we compute the ratio of the areas:
$\text{Ratio} = \frac{A_2}{A_1} = \frac{25\pi}{4\pi} = \frac{25}{4}$

The ratio $\frac{25}{4}$ simplifies to $6\frac{1}{4}$, indicating that the area of circle 2 is $6\frac{1}{4}$ times larger than the area of circle 1.

Therefore, the solution to the problem is $6\frac{1}{4}$.