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 900 inches to the power of 2
4 about 2,700 inches to the power of 2
We can use the formula for the area of a circle, which is A = πr^2, where r is the radius of the circle.
For circle A, we are given the diameter, which is 20 inches. Therefore, the radius would be half of that, which is 10 inches. We are also given that the area of circle A is 300 inches^2.
Plugging the values into the formula, we have:
300 = π(10)^2
300 = 100π
To find the value of π, we divide both sides by 100:
3 = π
Now let's find the radius of circle B given its diameter of 60 inches:
Radius = 60/2 = 30 inches
Now, let's calculate the areas of circle B using the formula:
1. Area = π(30)^2 ≈ 900π ≈ 2827.43 square inches
2. Area = π(30)^2 ≈ 900π ≈ 2827.43 square inches
3. Area = π(30)^2 ≈ 900π ≈ 2827.43 square inches
4. Area = π(30)^2 ≈ 900π ≈ 2827.43 square inches
Therefore, the area of circle B could be approximately 900 inches^2, which is option 3.