An arc of a circle of radius 13cm subtends angle 105 degrees at the center, calculate the length of arc, the perimeter of the sector and the area of the sector
Answers
23.8 = arc length
perimeter = 49.8 cm
area = 154.77 cm²
Step-by-step explanation:
2 π r (Ф /360) = arc
2 π *13 (105/360 )= arc
23.8 = arc length
Perimeter of sector = arc length + 2 r
= 23.8 cm + 2 * 13
= 23.8 + 26
= 49.8 cm
area = (Ф / 360 ) π *r*r
= 105 /360 * 3.14 *13*13
= 154.77 cm²
The length of an arc is = theta/360 x 2 π r
Given that a circle of radius 15 CM
Theta = 105°
To find 1st. Length of an arc
2nd. Perimeter of the corresponding sector (Length of an arc + 2 x r)
3rd. Area of the corresponding sector (Theta/360 x π r^2)
1st. Length of an arc = Theta/360 x 2 x π x r
=> 105/360 x 22/7 x 13
=> 11.91 cm...
2nd. Perimeter of the sector = Length of an arc + 2 x r
=> 11.91cm + 2 x 13cm
=> 37.91cm...
3rd. Area of the sector = Theta/360 x π x r^2
=> 105/360 x 22/ 7 x 13 x 13
=> 154.91cm^2
Hope you understood...
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