Marian drew a picture of two circles.She wanted to shade only the outer circle.
WHich of the following is closest to the area of the shaded region?
The shaded region of the outer circle's radius is 5 and the inside circl'es radius is 3
A.75
B.48
C.165
D.192
B?
Area =πr^2
π5^2 - π 3^2 = π (5^2 - 3^2) = ?
To find the area of the shaded region, we need to subtract the area of the inner circle from the area of the outer circle.
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the radius of the outer circle is 5 and the radius of the inner circle is 3, we can calculate their areas:
Area of outer circle = π(5^2) = 25π
Area of inner circle = π(3^2) = 9π
To find the area of the shaded region, we subtract the area of the inner circle from the area of the outer circle:
Shaded area = Area of outer circle - Area of inner circle = 25π - 9π = 16π
Now, we need to estimate the value of π. π is an irrational number approximately equal to 3.14. Let's use this approximation to find the estimated area of the shaded region:
Area of shaded region ≈ 16 × 3.14 ≈ 50.24
Among the given options, the closest area to 50.24 is option B: 48.
Therefore, option B is the closest to the area of the shaded region.