The area of a rectangle whose sides are 176 cm and 56 cm is equal to the area of a circle. What is the circumference (in cm) of the circle ? (Take $\pi =\frac{22}{7}$)

The correct answer is Option 2 (352).

Step 1: Calculate the area of the rectangle

Given the dimensions of the rectangle:

Length ($l$) = 176 cm

Breadth ($b$) = 56 cm

The formula for the area of a rectangle is:

$\text{Area of rectangle}=l\times b$

$\text{Area of rectangle}=176\times 56=9856{\text{cm}}^2$

Step 2: Find the radius of the circle

According to the problem statement, the area of the circle is equal to the area of the rectangle.

$\text{Area of circle}=\pi r^2$

$\pi r^2=9856$

Substitute $\pi =\frac{22}{7}$:

$\frac{22}{7}\times r^2=9856$

$r^2=\frac{9856\times 7}{22}$

$r^2=448\times 7$

$r^2=3136$

$r=\sqrt{3136}=56\text{cm}$

Step 3: Calculate the circumference of the circle

The formula for the circumference of a circle is:

$\text{Circumference}=2\pi r$

Substituting the values:

$\text{Circumference}=2\times \frac{22}{7}\times 56$

$\text{Circumference}=2\times 22\times 8=352\text{cm}$

Thus, the circumference of the circle is 352 cm.