Find the area of a minor sector of a circle whose circumference is 88 cm and the length of its minor arc is 22 cm (use $\pi =\frac{22}{7}$ ).

The correct answer is 154 cm².

Step-by-Step Explanation:

We are given the following information about a circle:

• Circumference of the circle ($C$) = 88 cm
• Length of the minor arc ($l$) = 22 cm
• Value of $\pi =\frac{22}{7}$

Step 1: Find the radius ($r$) of the circle

The formula for the circumference of a circle is:

$C=2\pi r$

Substituting the given values into the formula:

$88=2\times \frac{22}{7}\times r$

$88=\frac{44}{7}\times r$

Solving for $r$:

$r=\frac{88\times 7}{44}$

$r=2\times 7=14\text{cm}$

Step 2: Find the area of the minor sector

The area of a sector can be calculated directly using the length of the arc ($l$) and the radius ($r$) of the circle with the formula:

$\text{Area of sector}=\frac{1}{2}\times l\times r$

Substituting the values of $l=22\text{cm}$ and $r=14\text{cm}$:

$\text{Area of sector}=\frac{1}{2}\times 22\times 14$

$\text{Area of sector}=11\times 14=154{\text{cm}}^2$

Thus, the area of the minor sector is 154 cm².