A wire is in the form of a square of side 33 cm. If the wire is molded to form a circle, then what is the radius of the circle? ( Use ` pi = (22)/(7)`)

Options

A. 21 cm
B. 33 cm
C. 16.5 cm
D. 42 cm

Answer

To solve the problem step by step, we need to follow these instructions:

### Step 1: Calculate the perimeter of the square
The perimeter (P) of a square can be calculated using the formula:
\[ P = 4 \times \text{side} \]
Given the side of the square is 33 cm, we can calculate:
\[ P = 4 \times 33 \]
\[ P = 132 \text{ cm} \]

### Step 2: Understand that the perimeter of the square becomes the circumference of the circle
When the wire is molded into a circle, the perimeter of the square becomes the circumference (C) of the circle. Therefore:
\[ C = 132 \text{ cm} \]

### Step 3: Use the formula for the circumference of a circle to find the radius
The circumference of a circle is given by the formula:
\[ C = 2 \pi r \]
Where \( r \) is the radius of the circle. We can rearrange this formula to solve for \( r \):
\[ r = \frac{C}{2 \pi} \]

### Step 4: Substitute the values into the formula
Now we can substitute the values we have:
\[ r = \frac{132}{2 \times \frac{22}{7}} \]

### Step 5: Simplify the expression
First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now substitute this back into the radius formula:
\[ r = \frac{132}{\frac{44}{7}} \]

### Step 6: Multiply by the reciprocal
To divide by a fraction, we multiply by its reciprocal:
\[ r = 132 \times \frac{7}{44} \]

### Step 7: Simplify the multiplication
Now, simplify \( 132 \div 44 \):
\[ 132 \div 44 = 3 \]
So:
\[ r = 3 \times 7 = 21 \text{ cm} \]

### Final Answer
The radius of the circle is \( 21 \text{ cm} \).

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