Question

Area of sector of a circle with radius 18 cm is 198 cm\(^2\). The measure of central angle is

• A. \(70^\circ\)
• B. \(14^\circ\)
• C. \(140^\circ\)
• D. \(210^\circ\)

Hint:

Before multiplying out large numbers, always check if they can be cancelled with the opposite side of the equation.
In this problem, the product \(22 \times 9 = 198\) cancels out perfectly with the \(198\) on the left side, saving you from doing long division!

Answer 1

The Correct Option is A

Step 1: Find the area of the whole circle first.
\[ \text{Full circle area} = \pi r^2 = \frac{22}{7} \times 18 \times 18 = \frac{7128}{7}\ \text{cm}^2 \]
Step 2: Compare the sector's area to the full circle as a fraction.
The sector occupies the same fraction of the circle as its angle does out of $360^\circ$:
\[ \frac{198}{7128/7} = \frac{\theta}{360^\circ} \]
Step 3: Solve for the angle.
\[ \theta = \frac{198 \times 7 \times 360}{7128} = \frac{498960}{7128} = 70^\circ \]
\[ \boxed{\theta = 70^\circ} \]