Question

In the concentric circles shown, R represents the radius of

the larger circle and r represents the radius of the smaller
circle. Suppose that R 5 8 centimeters and r 5 3 centimeters.
Calculate the area of the shaded region.

Answer 1

To calculate the area of the shaded region, find the area of the larger circle and subtract the area of the smaller circle.

Step-by-step explanation:

To calculate the area of the shaded region, we need to find the area of the larger circle and subtract the area of the smaller circle. The formula to find the area of a circle is A = πr², where r is the radius.

For the larger circle, the radius is R, which is 8 centimeters. So the area of the larger circle is A₁ = π(8)² = 64π square centimeters.

For the smaller circle, the radius is r, which is 3 centimeters. So the area of the smaller circle is A₂ = π(3)² = 9π square centimeters.

Now, to find the area of the shaded region, we can subtract the area of the smaller circle from the area of the larger circle: A = A₁ - A₂ = 64π - 9π = 55π square centimeters.

Since π is a non-terminating decimal, we can approximate the area to a specific decimal place or leave it in terms of π.