What is the area of the shaded region in the given circle in terms of and in simplest form?
(1 point)
Responses
(120 + 6) m2
(120 Image with alt text: symbol pi + 6 Image with alt text: Start Root 3 End Root ) m 2
(96 + 36) m2
(96 Image with alt text: symbol pi + 36 Image with alt text: Start Root 3 End Root ) m 2
(120 + 36) m2
(120 Image with alt text: symbol pi + 36 Image with alt text: Start Root 3 End Root ) m 2
(96 + 6) m2
(120 + 36) m2
(120π + 36√3) m^2
how did you get that answer?
To find the area of the shaded region in the given circle, you need to subtract the area of the smaller circle from the area of the larger circle.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
Given that the radius of the larger circle is 6 units, and the radius of the smaller circle is 3 units (half the radius of the larger circle), we can calculate the area of the shaded region as follows:
Area of larger circle = π * (6)^2 = 36π
Area of smaller circle = π * (3)^2 = 9π
Area of shaded region = Area of larger circle - Area of smaller circle
= 36π - 9π
= 27π
So, the area of the shaded region in terms of π is:
27π square units
Therefore, the correct option is:
(120 + 36) m^2
(120π + 36√3) m^2