one circle has a diameter of 10 inches. a second circle has a diameter that is twice the diameter of the first circle What is the ratio of the area of the smaller circle to the larger circle
A1 = pi*5^2 = ? = 25pi
A2 = pi*10^2 = ? = 100pi
Looks like 4 times.
To find the ratio of the area of the smaller circle to the larger circle, we need to compare the areas of the two circles.
The area of a circle is given by the formula A = πr², where A represents the area and r represents the radius.
In the first circle, the diameter is 10 inches, which means the radius is half of the diameter, so the radius (r1) is 10/2 = 5 inches.
The area of the first circle (A1) can be calculated as follows:
A1 = π(5)² = 25π square inches.
In the second circle, the diameter is twice the diameter of the first circle, meaning the radius of the second circle (r2) is 2 times the radius of the first circle, so r2 = 5 * 2 = 10 inches.
The area of the second circle (A2) can be calculated as follows:
A2 = π(10)² = 100π square inches.
Now, we can find the ratio of the area of the smaller circle (A1) to the larger circle (A2):
Ratio = A1/A2 = (25π) / (100π) = 25/100 = 1/4.
Therefore, the ratio of the area of the smaller circle to the larger circle is 1/4.
To find the ratio of the area of the smaller circle to the larger circle, we need to calculate the areas of both circles and then divide the smaller circle's area by the larger circle's area.
First, let's start by finding the area of the smaller circle. The area of a circle can be calculated using the formula: A = π * r^2, where A is the area and r is the radius.
Since we know the diameter of the smaller circle is 10 inches, we can find its radius by dividing the diameter by 2. So, the radius (r) of the smaller circle is 10 inches / 2 = 5 inches.
Now let's calculate the area of the smaller circle using the formula: A = π * r^2
A = π * (5 inches)^2 = 25π square inches
Next, let's find the area of the larger circle. We know that the diameter of the larger circle is twice the diameter of the smaller circle, which means its diameter is 2 * 10 inches = 20 inches.
Similar to the process for the smaller circle, we can find the radius of the larger circle by dividing its diameter by 2. So, the radius (R) of the larger circle is 20 inches / 2 = 10 inches.
Now, let's calculate the area of the larger circle using the formula: A = π * R^2
A = π * (10 inches)^2 = 100π square inches
Finally, to find the ratio of the area of the smaller circle to the larger circle, we divide the area of the smaller circle (25π square inches) by the area of the larger circle (100π square inches):
Ratio = (Area of smaller circle) / (Area of larger circle)
Ratio = (25π square inches) / (100π square inches)
Now, we simplify the ratio:
Ratio = 25π / 100π
Ratio = 1/4
Therefore, the ratio of the area of the smaller circle to the larger circle is 1:4.