The ratio of the side of a square and the diameter of a circle is3:10. The circumference of circle is 220 metres. Find the area of the square

Options

A. 441 sq metres
B. 361 sq metres
C. 576 sq metres
D. 625 sq metres

Answer

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

### Step 1: Understand the given ratio
We know that the ratio of the side of a square (S) to the diameter of a circle (D) is given as 3:10. This can be expressed as:
\[ S : D = 3 : 10 \]

### Step 2: Express S and D in terms of a variable
Let’s represent the side of the square as \( S = 3x \) and the diameter of the circle as \( D = 10x \), where \( x \) is a common multiplier.

### Step 3: Find the radius of the circle
The radius \( r \) of the circle is half of the diameter:
\[ r = \frac{D}{2} = \frac{10x}{2} = 5x \]

### Step 4: Use the circumference of the circle
The circumference \( C \) of the circle is given as 220 meters. The formula for the circumference is:
\[ C = 2\pi r \]
Substituting the value of \( r \):
\[ 220 = 2 \times \frac{22}{7} \times 5x \]

### Step 5: Simplify the equation
Now, we can simplify the equation:
\[ 220 = \frac{220}{7} \times x \]
To eliminate the fraction, multiply both sides by 7:
\[ 220 \times 7 = 220x \]
\[ 1540 = 220x \]

### Step 6: Solve for x
Now, divide both sides by 220 to find \( x \):
\[ x = \frac{1540}{220} = 7 \]

### Step 7: Find the side of the square
Now that we have \( x \), we can find the side of the square:
\[ S = 3x = 3 \times 7 = 21 \text{ meters} \]

### Step 8: Calculate the area of the square
The area \( A \) of the square is given by:
\[ A = S^2 = 21^2 = 441 \text{ square meters} \]

### Conclusion
Thus, the area of the square is \( 441 \) square meters.

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