Question

A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is

• A. \(\frac{77}{4} \text{ cm}^2\)
• B. \(77 \text{ cm}^2\)
• C. \(154 \text{ cm}^2\)
• D. \(\frac{77}{8} \text{ cm}^2\)

Hint:

Calculating sector area can also be done using the central angle formula, but direct division is much faster and reduces decimal calculation errors!

Answer 1

The Correct Option is D

Step 1: Find the central angle of one sector.
A full circle is $360^\circ$ split into 16 equal sectors, so each sector's angle is $\theta = \frac{360^\circ}{16}=22.5^\circ$.
Step 2: Use the sector-area formula with this angle.
Area of one sector $=\frac{\theta}{360^\circ}\times\pi r^2 = \frac{22.5}{360}\times\frac{22}{7}\times7^2$.
Step 3: Simplify.
$\frac{22.5}{360}=\frac{1}{16}$ and $\frac{22}{7}\times49=154$, so the area is $\frac{154}{16}=\frac{77}{8}\text{ cm}^2$, matching option (D).
\[ \boxed{\frac{77}{8}\text{ cm}^2} \]