What would be the area of a rectangle whose area is equal to the area of a circle of radius 7 cm?

Options

A. `77 cm^2`
B. `154 cm^2`
C. `184 cm^2`
D. `180 cm ^2`

Answer

To find the area of a rectangle whose area is equal to the area of a circle with a radius of 7 cm, we can follow these steps:

### Step 1: Calculate the area of the circle
The formula for the area of a circle is given by:
\[ \text{Area of Circle} = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the radius into the formula
Given that the radius \( r = 7 \) cm, we can substitute this value into the formula:
\[ \text{Area of Circle} = \pi (7)^2 \]

### Step 3: Calculate \( 7^2 \)
Calculating \( 7^2 \):
\[ 7^2 = 49 \]

### Step 4: Substitute \( 49 \) into the area formula
Now, substituting \( 49 \) into the area formula:
\[ \text{Area of Circle} = \pi \times 49 \]

### Step 5: Use the value of \( \pi \)
For this problem, we will use the approximation \( \pi = \frac{22}{7} \):
\[ \text{Area of Circle} = \frac{22}{7} \times 49 \]

### Step 6: Simplify the expression
Now, we can simplify:
\[ \text{Area of Circle} = \frac{22 \times 49}{7} \]

### Step 7: Calculate \( \frac{49}{7} \)
Calculating \( \frac{49}{7} \):
\[ \frac{49}{7} = 7 \]

### Step 8: Substitute back to find the area
Now substituting back:
\[ \text{Area of Circle} = 22 \times 7 \]

### Step 9: Calculate \( 22 \times 7 \)
Calculating \( 22 \times 7 \):
\[ 22 \times 7 = 154 \]

### Conclusion
Thus, the area of the rectangle, which is equal to the area of the circle, is:
\[ \text{Area of Rectangle} = 154 \text{ cm}^2 \]

### Final Answer
The area of the rectangle is **154 cm²**.

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