The area of the largest circle that can be drawn inside a rectangle with sides 63 cm and 42 cm is (in $cm^2$) :
(Take $$ \pi = \frac{22}{7} $$)

Question

The area of the largest circle that can be drawn inside a rectangle with sides 63 cm and 42 cm is (in $cm^2$) :  
(Take $$ \pi = \frac{22}{7} $$)

Accepted Answer

1. **Identify the Largest Circle**:  
   The largest circle that can fit inside the rectangle will have its diameter equal to the smaller side of the rectangle (breadth).  
   - Given dimensions of the rectangle:  
     Length = 63 cm, Breadth = 42 cm.  
   - Diameter of the circle = Breadth = 42 cm.

2. **Calculate Radius**:  
   The radius of the circle is half of its diameter:  
   $$
   r = \frac{	ext{Diameter}}{2} = \frac{42}{2} = 21 \, 	ext{cm}.
   $$

3. **Calculate Area of the Circle**:  
   The formula for the area of a circle is:  
   $$
   A = \pi r^2.
   $$  
   Substituting $$ r = 21 $$ and $$ \pi = \frac{22}{7} $$:  
   $$
   A = \frac{22}{7} 	imes 21^2.
   $$  
   Simplify:  
   $$
   A = \frac{22}{7} 	imes 441 = 1386 \, 	ext{cm}^2.
   $$

Thus, the area of the largest circle is **$$ 1386 \, 	ext{cm}^2 $$**.

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