Question

Shown in the given figure is a circle with centre O. The area of the minor sector is 7 cm². Area of circle is:

Options

• 84 π cm²

• `84/11  cm^2` 

• 84 cm²

• `sqrt84/pi  cm^2` 

Answer 1

84 cm²

Explanation:

Given: θ = 30°

Area of minor sector = 7 cm²

The area of a sector is a fraction of the total area of the circle. This fraction is determined by the central angle θ compared to the full 360° of the circle.

Area of Sector = `(θ/(360°)) xx "Area of Circle"`

7 = `(30°)/(360°) xx "Area of Circle"`

7 = `1/12 xx "Area of Circle"`

Area of Circle = 12 × 7

= 84 cm²