Question

Shown in the given figure is a circle with centre \(O\). The area of the minor sector is \(7 \text{ cm}^{2}\). Area of circle is :

• A. \(84 \pi \text{ cm}^{2}\)
• B. \(\frac{84}{11} \text{ cm}^{2}\)
• C. \(84 \text{ cm}^{2}\)
• D. \(\frac{\sqrt{84}}{\sqrt{\pi}} \text{ cm}^{2}\)

Hint:

If the sector angle is \(30^{\circ}\), there are \(360/30 = 12\) such sectors in a circle. Just multiply the sector area by 12 to get the full circle area.

Answer 1

The Correct Option is C

To find the area of the circle, we need to use the information given about the minor sector. We have:

• The area of the minor sector is \(7 \, \text{cm}^2\).
• The central angle of the sector is \(30^\circ\).

The formula for the area of a sector is:

\(A_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2\)

where \(\theta = 30^\circ\) and \(A_{\text{sector}} = 7 \, \text{cm}^2\).

Substituting the values, we get:

\(7 = \frac{30}{360} \times \pi r^2\)

Simplifying, we have:

\(7 = \frac{1}{12} \times \pi r^2\)

Therefore,

\(\pi r^2 = 7 \times 12\)

\(\pi r^2 = 84 \, \text{cm}^2\)

Hence, the area of the circle is \(84 \, \text{cm}^2\).

The correct answer is: \(84 \, \text{cm}^2\).