A sector of a circle of radius 7cm subtends angle 270° at the centre. Calculate a. Length of arc b. Area of sector c. Perimeter of sector
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To calculate the length of the arc of a sector, you can use the formula:
Arc Length = (θ/360) x 2πr
Where θ is the angle in degrees, and r is the radius.
a. Length of arc:
In this case, the angle θ is 270° and the radius r is 7cm.
Using the formula, we can calculate it as follows:
Arc Length = (270/360) x 2π(7)
Arc Length = (3/4) x 2π(7)
Arc Length = (3/4) x (22/7) x 7
Arc Length = 3 x 2 x 7
Arc Length = 42 cm
Therefore, the length of the arc is 42 cm.
b. Area of the sector:
The formula to calculate the area of a sector is:
Area = (θ/360) x πr^2
Using the given values:
Area = (270/360) x π(7^2)
Area = (3/4) x π(49)
Area = (3/4) x (22/7) x 49
Area = 3 x 2 x 49
Area = 294 cm^2
Therefore, the area of the sector is 294 cm^2.
c. Perimeter of the sector:
The perimeter of a sector is the sum of the arc length and the two radii of the sector.
Perimeter = Arc Length + 2r
Using the given values:
Perimeter = 42 + 2(7)
Perimeter = 42 + 14
Perimeter = 56 cm
Therefore, the perimeter of the sector is 56 cm.
easy way: 270° is 3/4 of a circle, so the
arc is 3/4 * 2πr
area is 3/4 * πr^2
But, using the same logic, you have 270/360 * 2π = 3π/2, so
arc is rθ = 3 * 3π/2
area is 1/2 r^2 θ = 1/2 * 9 * 3π/2
perimeter = arc + 2 radii = 9π/4 + 2*3