The radii of two concentric circles are 4 cm and 5 cm. The difference in the areas of these two circles is :

Options

A. `pi`
B. `7 pi`
C. `9 pi`
D. `13 pi`

Answer

To find the difference in the areas of two concentric circles with radii of 4 cm and 5 cm, we can follow these steps:

### Step 1: Identify the radii of the circles.
- The radius of the first circle (C1) is 5 cm.
- The radius of the second circle (C2) is 4 cm.

### Step 2: Use the formula for the area of a circle.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 3: Calculate the area of the larger circle (C1).
Using the radius of the first circle (5 cm):
\[ A_{C1} = \pi (5)^2 = \pi \times 25 = 25\pi \, \text{cm}^2 \]

### Step 4: Calculate the area of the smaller circle (C2).
Using the radius of the second circle (4 cm):
\[ A_{C2} = \pi (4)^2 = \pi \times 16 = 16\pi \, \text{cm}^2 \]

### Step 5: Find the difference in the areas.
To find the difference in the areas of the two circles, subtract the area of the smaller circle from the area of the larger circle:
\[ \text{Difference} = A_{C1} - A_{C2} = 25\pi - 16\pi = (25 - 16)\pi = 9\pi \, \text{cm}^2 \]

### Final Answer:
The difference in the areas of the two circles is \( 9\pi \, \text{cm}^2 \).

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