Question

Find area of a sector of circle with radius 7cm and length of the arc corresponding to the sector is 10cm​

Answer 1

Step-by-step explanation:

Given:

Radius 7cm

length of the arc corresponding to the sector is 10cm.

To find:Area of a sector of circle

Solution:

Tip: Find the angle of sector subtended at centre of circle from arc length,then find Area of sector.

Formula to find arc length:

$= \frac{ \theta}{360} \times 2\pi \: r \\ \\ 10 = \frac{ \theta}{360} \times 2\ \times \frac{22}{7} \: \times 7 \\ \\ 10 = \frac{44 \: \theta}{360} \\ \\ \theta = \frac{10 \times 360}{44} \\ \\ \theta = \frac{3600}{44}$

Find Area of sector:

$area \: of \: sector = \frac{ \theta}{360} \times \pi \times {r}^{2} \\ \\ = \frac{ 3600}{44 \times 360} \times \ \frac{22}{7} \times {(7)}^{2} \\ \\ = \frac{ 5 \: \cancel{10}}{ \cancel2 \: \cancel{44}} \times \frac{ \cancel{ 22}}{ \cancel7} \times 7 \: \cancel{49} \\ \\ = 5 \times 7 \\ \\ = 35 \: {cm}^{2}$

Thus,

Area of sector corresponding to given arc length is 35 sq-cm.

Hope it helps you.

To learn more on Brainly:

1)Find the area of sector of a circle with radius 7 cm if the angle of the sector is 60 degree.

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