Question

Let BC=CD=12cm, and the length of arc BD=15cm. Find the area, in square centimeters, of sector BCD.

Answer 1

option b : 90 sq. cm

Explanation:

1) Area of circle with radius = 12cm

Area = π r^2

= 3.14 * (12) (12)

= 3.14 * 144

= approx 452.4

2) Circumference of circle with radius = 12cm

Circumference = 2πr

= 2 * 3.14 * 12

= approx 75 .4

3) Arc length = 15cm ......(given)

`(area \: of \: sector)/(total \: area) = (arc \: length)/(circumference)`

`(area \: of \: sector)/(452.4) = (15)/(75.4)`

`area \: of \: sector \: = (15 * 452.4)/(75.4)`

`= (6786)/(75.4)`

`= 90 {cm}^(2)`