Find the area of a quadrant of a circle whose circumference is 88 cm.
Quadrant is a sector in which the central angle is 90 degrees, and this is the key to solve this question. As we know the central angle of the sector so we can easily calculate the area of quadrant by first calculating the radius of the circle as the circumference of the circle is given and then applying the formula of area of sector.
So, we know Circumference of a circle = 2πR → eqn1
Where R = radius of the circle
Given Circumference of the circle = 88 cm, θ = 90°
Put the given values in equation 1
⟹ 88 = (44×R)/7
⟹ 88 = 44R/7
⟹ (88×7)/44 = R
⟹ 616/44 = R
⇒ R = 14 cm
Put the values of R and θ in the above equation
= 154 cm2.
The area of quadrant is 154 cm2.