circle A has a diameter of approximately 20 inches and an area of 300 inches to the power of 2.
circle B has a diameter of approximately 60 inches.
which of these could be the area of circle B? explain your reasoning.
1. about 100 inches to the power of 2
2. about 300 inches to the power of 2
3. about 2,700 inches to the power of 2
To find the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius.
For circle A with a diameter of 20 inches, the radius is half of the diameter, so r = 10 inches.
We are given that the area of circle A is 300 inches^2, so we can calculate:
300 = π(10)^2
300 = 100π
π ≈ 3.14
Now, let's consider circle B with a diameter of 60 inches. Using the same formula, we can calculate the potential areas:
1. If circle B had an area of approximately 100 inches^2, we need to determine the radius, r. Since the formula uses the radius, we divide the diameter by 2: r = 60/2 = 30 inches.
Now, we can calculate the area:
A = π(30)^2
A = 900π
Using π ≈ 3.14, the area is approximately 2,826 inches^2.
Therefore, option 1 is not a possible area for circle B.
2. If circle B had an area of approximately 300 inches^2, using the same method as in option 1, we calculate:
A = π(30)^2
A = 900π
Using π ≈ 3.14, the area is approximately 2,826 inches^2.
Therefore, option 2 is also not a possible area for circle B.
3. If circle B had an area of approximately 2,700 inches^2, using the same method as in the previous options:
A = π(30)^2
A = 900π
Using π ≈ 3.14, the area is approximately 2,826 inches^2.
Therefore, option 3 is a possible area for circle B.
To summarize, the only possible area for circle B is approximately 2,700 inches^2, which is option 3.