the circle below has a radius of 10 cm. what is the area of the shaped region ? if necessary, round your answerto two decimal places. do not include units in your answer
We can't see the area of the shaped region.
56
To find the area of the shaped region in the circle, we need to follow these steps:
1. Determine the area of the entire circle using the formula: A = πr^2, where A is the area and r is the radius.
2. Calculate the area of the shaded region (which is the difference between the area of the entire circle and the area of the inner circle).
Let's calculate it step by step:
1. Calculate the area of the entire circle:
A = πr^2
A = π(10 cm)^2
A = π(100 cm^2) [Using the formula A = πr^2]
A ≈ 314.16 cm^2 [Approximating π value to two decimal places]
2. Calculate the area of the inner circle (which represents the shaded region):
A_inner circle = πr_inner circle^2
Since the inner circle is smaller than the entire circle, its radius is half of the radius of the outer circle.
r_inner circle = r/2
r_inner circle = 10 cm/2
r_inner circle = 5 cm
A_inner circle = π(5 cm)^2
A_inner circle = π(25 cm^2) [Using the formula A = πr^2]
A_inner circle ≈ 78.54 cm^2 [Approximating π value to two decimal places]
3. Calculate the area of the shaded region (difference between the areas of the entire circle and the inner circle):
Area of shaded region = Area of the entire circle - Area of the inner circle
= 314.16 cm^2 - 78.54 cm^2
= 235.62 cm^2
Thus, the area of the shaped region in the circle is approximately 235.62 cm^2.