Concentric Area Game

Concentric Area Game
When you have two concentric circles (circles that share the same center), the shaded region between them forms a ring, which is called an annulus. To find the area of the annulus, you find the area of the larger circle and subtract the area of the smaller circle. Scroll down the page for a more detailed explanation.
 
This game will give you two concentric circles, and you’ll have to find the shaded area. If you give a wrong answer, the game will give you the right answer.
 
Area of Shaded Region (Rectangle in a rectangle)
Area of Shaded Region (Circle in a rectangle)
Inscribed Area (Inscribed Circle in Square)
Concentric Area (Circle in a Circle)
 

Score: 0 / 0

Time: 00:00

Menu

Find the Shaded Area

Use 3.14 for π. Round to 2 decimal places.

Check Next Finish

Concentric Area!

Find the area of the shaded ring.

Start Game

 

How to Play the Concentric Area Game
In this game, you need to find the area of the shaded region between two concentric circles. You may use the subtraction method. Subtract the area of the smaller circle from the area of the bigger circle.
Here’s how to play:

1. Start Game: Click start game.
   
2. Look at the Figure: Find the area of the shaded region.
   
3. Enter Your Answer: Type your answer for the area.
   
4. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
5. Get a New Problem: Click the Next Problem button (or press Enter again) for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Restart Game Click “Restart Game” to restart the game.
    
   

Finding the Area of a Square with an Inscribed Circular Hole
Area of the Shaded Region Between Two Concentric Circles
The shaded region between two concentric circles (an annulus) is calculated by finding the difference between the area of the outer circle and the area of the inner circle.
The Formula
Let R be the radius of the Outer Circle and r be the radius of the Inner Circle.

1. Area of the Outer Circle (A_R):
   A_R = πR²
   
2. Area of the Inner Circle (A_r):
   A_r = πr²
   
3. Area of the Annulus (A):
   Area (A) = A_R - A_r
   By factoring out $\pi$, we get the general formula for the area of an annulus:
   A = π(R² - r²)
    
   

The video gives a clear, step-by-step approach to find the area of shaded region in concentric circles.

• Show Video

 

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