Evaluate the area of the largest circle that can be inscribed inside a rectangle of sides 7 cm and 3.5 cm.

Options

A. `12/7 cm^2`
B. `17/7 cm^2`
C. `77/8 cm^2 `
D. `22/7 cm^2`

Answer

To find the area of the largest circle that can be inscribed inside a rectangle with sides 7 cm and 3.5 cm, we can follow these steps:

### Step 1: Determine the diameter of the inscribed circle
The largest circle that can be inscribed in a rectangle will have a diameter equal to the shorter side of the rectangle. In this case, the sides of the rectangle are 7 cm and 3.5 cm. Therefore, the diameter of the circle is:

\[ \text{Diameter} = 3.5 \, \text{cm} \]

### Step 2: Calculate the radius of the circle
The radius of the circle is half of the diameter. Thus, we can calculate the radius as follows:

\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{3.5 \, \text{cm}}{2} = 1.75 \, \text{cm} \]

### Step 3: Calculate the area of the circle
The area \(A\) of a circle is given by the formula:

\[ A = \pi r^2 \]

Substituting the radius we found:

\[ A = \pi (1.75 \, \text{cm})^2 \]

Calculating \( (1.75)^2 \):

\[ (1.75)^2 = 3.0625 \]

Now substituting back into the area formula:

\[ A = \pi \times 3.0625 \, \text{cm}^2 \]

Using \( \pi \approx 3.14 \):

\[ A \approx 3.14 \times 3.0625 \approx 9.62875 \, \text{cm}^2 \]

### Step 4: Round the answer
Rounding the area to two decimal places, we get:

\[ A \approx 9.63 \, \text{cm}^2 \]

### Final Answer
The area of the largest circle that can be inscribed inside the rectangle is approximately:

\[ \boxed{9.63 \, \text{cm}^2} \]

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