Q.1.Calculate the length of an are of a circle of radius 6 cm if the angle it subtends at the centre of circle is 6o. Q.2. Find the perimeter of a sector of a circle radius 5.2cm if the angle subtend at the centre is (a)3o (b)6o (c)135.
Is this geometry? The name of your school does not let a tutor know what SUBJECT you need help in.
To calculate the length of an arc of a circle, you need to use the formula:
Arc Length = (Angle/360) * 2πr
where 'Angle' is the measure of the angle subtended by the arc at the center of the circle, and 'r' is the radius of the circle.
Let's solve the first question:
Q1. Calculate the length of an arc of a circle with a radius of 6 cm if the angle it subtends at the center of the circle is 60°.
Using the formula, we have:
Arc Length = (60/360) * 2π * 6
= (1/6) * 2π * 6
= (1/6) * 12π
= 2π cm
≈ 6.28 cm
Therefore, the length of the arc is approximately 6.28 cm.
Now let's move on to the second question:
Q2. Find the perimeter of a sector of a circle with a radius of 5.2 cm, given the angle subtended at the center is (a) 3° (b) 6° (c) 135°.
To find the perimeter of a sector of a circle, you need to add the length of the arc and the lengths of the two radii forming the sector.
(a) For an angle of 3°:
Arc Length = (3/360) * 2π * 5.2
≈ 0.054 cm
Perimeter = Arc Length + 2r
≈ 0.054 + 2 * 5.2
≈ 0.054 + 10.4
≈ 10.454 cm
Therefore, the perimeter of the sector for an angle of 3° is approximately 10.454 cm.
(b) For an angle of 6°:
Arc Length = (6/360) * 2π * 5.2
≈ 0.109 cm
Perimeter = Arc Length + 2r
≈ 0.109 + 2 * 5.2
≈ 0.109 + 10.4
≈ 10.509 cm
Therefore, the perimeter of the sector for an angle of 6° is approximately 10.509 cm.
(c) For an angle of 135°:
Arc Length = (135/360) * 2π * 5.2
≈ 4.9 cm
Perimeter = Arc Length + 2r
≈ 4.9 + 2 * 5.2
≈ 4.9 + 10.4
≈ 15.3 cm
Therefore, the perimeter of the sector for an angle of 135° is approximately 15.3 cm.