a target consists of five concentric circles, each with a radius 1 inch longer than that of the previous circle. calculate the area between the third and fourth circles from the center.
What is the radius of the smallest circle?
the radius of the smallest circle is one inch
A = pi * r^2
3rd circle:
A = 3.14 * 9
A = 28.26 sq. inches
4th circle:
A = 3.14 * 16
A = 50.24 sq. in.
50.24 - 28.26 = ?
To calculate the area between the third and fourth circles from the center, we need to determine the areas of both circles and then find the difference between them.
First, let's find the radius of the third circle. We know that each circle has a radius 1 inch longer than the previous circle. Since the first circle's radius is not given, we'll assume it to be r inches.
So the radius of the third circle would be (r + 2) inches. Similarly, the radius of the fourth circle would be (r + 3) inches.
Now, let's calculate the areas of the third and fourth circles.
The formula to find the area of a circle is A = π * r^2, where A is the area and r is the radius.
The area of the third circle would be A3 = π * (r + 2)^2, and the area of the fourth circle would be A4 = π * (r + 3)^2.
To find the area between the third and fourth circles, we subtract the area of the third circle from the area of the fourth circle:
Area = A4 - A3
Substituting the formulas for A3 and A4:
Area = π * (r + 3)^2 - π * (r + 2)^2
To simplify further, we can expand the square terms:
Area = π * (r^2 + 6r + 9) - π * (r^2 + 4r + 4)
Now, we can combine the terms:
Area = π * r^2 + 6πr + 9π - π * r^2 - 4πr - 4π
Simplifying again:
Area = 2πr + 5π
So, the area between the third and fourth circles from the center is 2πr + 5π, where r is the radius of the first circle (which was assumed).