Find the area of the space enclosed by two concentric circles of radii 25 cm and 17 cm.

Answer

To find the area of the space enclosed by two concentric circles with radii 25 cm and 17 cm, we can follow these steps:

### Step 1: Identify the Radii
Let the radius of the larger circle (R) be 25 cm and the radius of the smaller circle (r) be 17 cm.

### Step 2: Calculate the Area of the Larger Circle
The formula for the area of a circle is given by:
\[ \text{Area} = \pi R^2 \]
Substituting the value of R:
\[ \text{Area of larger circle} = \pi (25)^2 = \pi \times 625 \]

### Step 3: Calculate the Area of the Smaller Circle
Using the same formula for the smaller circle:
\[ \text{Area of smaller circle} = \pi r^2 = \pi (17)^2 = \pi \times 289 \]

### Step 4: Find the Area Enclosed Between the Two Circles
To find the area of the space enclosed between the two circles, we subtract the area of the smaller circle from the area of the larger circle:
\[ \text{Area enclosed} = \text{Area of larger circle} - \text{Area of smaller circle} \]
\[ = \pi \times 625 - \pi \times 289 \]
\[ = \pi (625 - 289) \]
\[ = \pi \times 336 \]

### Step 5: Substitute the Value of π
Using \( \pi \approx \frac{22}{7} \):
\[ \text{Area enclosed} = \frac{22}{7} \times 336 \]

### Step 6: Simplify the Calculation
First, divide 336 by 7:
\[ 336 \div 7 = 48 \]
Now multiply by 22:
\[ 48 \times 22 = 1056 \]

### Step 7: Write the Final Answer
Thus, the area of the space enclosed by the two circles is:
\[ \text{Area} = 1056 \, \text{cm}^2 \]

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