Question

7) The length of an arc of a circle subtending an angle of
measure 60° at the center is 10 cm. Find the area and
the circumference of the circle.
​

Answer 1

Step-by-step explanation:

$\underline{ \green{ \sf \: Given:-}}$

• Theta
• Radius

$\underline{ \green{ \sf \: To \: Find:-}}$

• The area and the circumference

$\underline{ \green{ \sf \: Solution:-}}$

$\tt \: Area = \bigg(\frac{60} {360} \times \pi {r}^{2} \bigg) \\ \tt \leadsto \: \frac{1}{ \cancel6} \times \frac{ \cancel{22}}{7} \times 10 \times 10 \\ \tt \leadsto \: \frac{1 \times 11 \times 10 \times 10}{21} \\ \\ \tt \leadsto \: \red{\frac{1100}{21} = 52.38 \: {cm}^{2} (approx.) }$

$\tt \: Circumference = \frac{60}{360} \times 2\pi r \\ \leadsto \tt \: \frac{1}{ \cancel{6}} \times 2 \times \frac{22}{7} \times \cancel{10 }\\ \tt \leadsto \frac{1 \times 2 \times 22 \times 5}{21} \\ \purple{\tt \leadsto \: \frac{220}{21} = 10.476 \: cm(approx.)}$