Calculate the perimeter of a sector of a circle whose radius is 6cm and the angle substended at the centre is 90degree
90 degrees is a quarter of 360
so
perimeter of sector = (1/4) ( 2 pi R)
88/7cm
Using the formula, we have:
perimeter of sector = (1/4) (2 π R)
Substituting R = 6 cm and π = 22/7, we get:
perimeter of sector = (1/4) (2 × 22/7 × 6)
perimeter of sector = (1/4) (44/7 × 3)
perimeter of sector = (1/4) (132/7)
perimeter of sector = 33/7 cm
Therefore, the perimeter of the sector is 33/7 cm or approximately 4.71 cm (rounded to two decimal places).
To calculate the perimeter of a sector of a circle, the first step is to find the length of the curved arc that makes up the sector.
The perimeter of a sector is given by the formula: Perimeter = (angle/360) * 2πr
In this case, the radius of the circle is given as 6 cm, and the angle subtended at the center is 90 degrees.
Plugging in the values into the formula, we have:
Perimeter = (90/360) * 2π * 6
First, simplify the fraction:
Perimeter = (1/4) * 2π * 6
Multiplying the fractions and simplifying further:
Perimeter = (1/2)π * 6
Now, multiply the radius with the simplified fraction:
Perimeter = (1/2) * 6π
Finally, evaluate the expression:
Perimeter = 3π
Therefore, the perimeter of the sector is 3π cm.