the diagram shows a sector of a circle radius 10cm find the perimeter of the sector giving your answer correct to 1 decimal place
Answers
Answer:
The perimeter is 43.6 cm
Step-by-step explanation:
In this question, we are tasked with calculating the perimeter of the sector.
Firstly, we define what a sector is. A sector is part of a circle which is is blinded by two radii and an arc. Hence we say a sector contains two radii.
Thus, to calculate the perimeter of the sector, we need the length of the arc added to 2 * length of the radius
Let’s calculate the length of the arc.
Mathematically, this is theta/360 * 2 * pi * r
where theta is the angle subtended at the middle of the circle which is 135 according to the question, and our radius is 10cm
Thus, we have
135/360 * 2 * 22/7 * 10 = 23.57 cm
Adding two radii to this, we have;
23.57 + 2(10)
= 23.57 + 20 = 43.57 = 43.6 cm to 1 decimal place
Given : The diagram shows a sector of a circle radius 10cm
To find : the perimeter of the sector
Solution:
Perimeter of the sector = Radius + arc length + radius
Radius = 10 cm
=> Perimeter of the sector = 10 + arc length + 10
=> Perimeter of the sector = 20 + arc length
arc length = (sector angle/ 360° ) * perimeter of the circle
Perimeter of a circle = 2πr
sector angle = 135°
arc length = (135°/ 360° ) * 2π(10)
= (3/8) 20π
= 15π/2
Using π = 3.14
= 15 * 3.14 /2
= 23.55
Perimeter of the sector = 20 + 23.55
= 43.55
= 43.6 cm
perimeter of the sector = 43.6 cm
Learn More:
Which has greater degree measure : an arc of length 5cm of circle of ...
brainly.in/question/13827112
in the given figure, 'O' is the centre of the circle and the length of arc ...
brainly.in/question/14816480
