Two circles with radii of 3cm and 4cm what is the ratio of the area?

ratio of their areas = 3^2 : 4^2

= 9 : 16

areas of circles = proportional to the square of their radii

Well, circles are like edible pizzas, so let's compare these two delicious pizzas. The first pizza has a radius of 3cm, so its area is like a small cheesy bite. The second pizza has a radius of 4cm, so it's a slightly bigger and more satisfying slice.

To find the ratio of the areas, we simply divide the area of the second pizza by the area of the first pizza. Using the formula for the area of a circle (A = πr²), the area of the first pizza is π(3)² = 9π cm², and the area of the second pizza is π(4)² = 16π cm².

Now, we divide 16π cm² by 9π cm², and we get 16/9. So, the ratio of the areas is 16:9. It's like saying the second pizza is 16/9 times bigger than the first pizza.

To find the ratio of the areas of two circles with radii of 3 cm and 4 cm, you can use the formula for the area of a circle:

Area = π * radius^2.

First, let's calculate the area of the two circles:

For the circle with a radius of 3 cm:
Area1 = π * (3 cm)^2
= 9π cm^2

For the circle with a radius of 4 cm:
Area2 = π * (4 cm)^2
= 16π cm^2

Now, we can find the ratio of the two areas:

Ratio = Area1 / Area2
= (9π cm^2) / (16π cm^2)

The π cancels out, leaving us with:
Ratio = 9/16

Therefore, the ratio of the areas of the two circles is 9:16.

To find the ratio of the areas of the two circles, we need to divide the area of the larger circle by the area of the smaller circle.

The formula for the area of a circle is given by \(A = \pi r^2\), where \(A\) represents the area and \(r\) represents the radius.

Let's calculate the areas of the two circles and find their ratio:

1. Area of the first circle:
\(A_1 = \pi r_1^2\)
\(A_1 = \pi (3\,cm)^2\)
\(A_1 = \pi (9\,cm^2)\)
\(A_1 \approx 28.27\,cm^2\) (rounded to two decimal places)

2. Area of the second circle:
\(A_2 = \pi r_2^2\)
\(A_2 = \pi (4\,cm)^2\)
\(A_2 = \pi (16\,cm^2)\)
\(A_2 \approx 50.27\,cm^2\) (rounded to two decimal places)

Now, we can calculate the ratio of the areas by dividing the larger area by the smaller area:

\(\text{Ratio} = \frac{A_2}{A_1}\)
\(\text{Ratio} = \frac{50.27\,cm^2}{28.27\,cm^2}\)
\(\text{Ratio} \approx 1.78\) (rounded to two decimal places)

Therefore, the ratio of the areas of the two circles with radii 3cm and 4cm is approximately 1.78.