https://file.aiquickdraw.com/mathbot/file/172719074630756nzchog.jpg

To solve the problem of finding the area of the ring-shaped region (or annulus), we need to calculate the difference between the areas of two circles: the outer circle and the inner circle.

The formula for the area \( A \) of a circle is:

\[
A = \pi r^2
\]

where \( r \) is the radius of the circle.

### Step 1: Calculate the area of the outer circle
The radius of the outer circle is 25 inches.

\[
A_{\text{outer}} = \pi (25)^2 = 625\pi \, \text{square inches}
\]

### Step 2: Calculate the area of the inner circle
The radius of the inner circle is 20 inches.

\[
A_{\text{inner}} = \pi (20)^2 = 400\pi \, \text{square inches}
\]

### Step 3: Find the area of the ring-shaped region
The area of the ring-shaped region is the difference between the outer and inner circle areas.

\[
A_{\text{ring}} = A_{\text{outer}} - A_{\text{inner}} = 625\pi - 400\pi = 225\pi \, \text{square inches}
\]

### Final Answer:
The area of the ring-shaped region is:

\[
A_{\text{ring}} = 225\pi \approx 706.86 \, \text{square inches}
\]

Let me know if you'd like more details on any part of this solution!

### Related Questions:
1. How would the area change if the inner radius were increased by 5 inches?
2. What is the circumference of both the outer and inner circles?
3. How do you calculate the area of an annulus if the radii are given in different units?
4. What would the area be if both radii were doubled?
5. How does the formula for the area of an annulus relate to other geometric shapes?

**Tip:** Always remember to use the same units throughout a calculation to avoid errors!

A ring-shaped region is shown. Its inner radius is 20 inches, and its outer radius is 25 inches. Find the area of the ring-shaped region.

Learn how to calculate the area of a ring-shaped region (annulus) with an inner radius of 20 inches and an outer radius of 25 inches. Using the formula for the area of a circle, find the difference between the areas of the outer and inner circles to get the area of the ring. Perfect for geometry students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation