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# A sector of a circle has an area of 55 cm2. If the radius of the circle is 10 cm...

### Question

A sector of a circle has an area of 55 cm2. If the radius of the circle is 10 cm, calculate the angle of the sector. [π = 22/7]

### Options

A) 45$$^{\circ}$$

B) 63$$^{\circ}$$

C) 75$$^{\circ}$$

D) 90$$^{\circ}$$

Area of a sector = $$\frac{\theta}{360}\times \pi r^2\\55=\frac{\theta}{360}\times \frac{22}{7}\times \frac{10\times 10}{1}\\\theta=\frac{360 \times 55 \times 7}{22 \times 10 \times 10}\\\theta = 63^{\circ}$$
• Area of a sector = $$\frac{\theta}{360}\times \pi r^2\\55=\frac{\theta}{360}\times \frac{22}{7}\times \frac{10\times 10}{1}\\\theta=\frac{360 \times 55 \times 7}{22 \times 10 \times 10}\\\theta = 63^{\circ}$$