Find the difference of the areas of a sector | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that,the radius of the circle $(r) = 21 \, cm$ and the central angle of the minor sector $(	heta) = 120^{\circ}$.First,calculate the total

Vedclass · Accepted Answer

$462$

Vedclass · Answer

(C) Given that,the radius of the circle $(r) = 21 \, cm$ and the central angle of the minor sector $(	heta) = 120^{\circ}$.First,calculate the total area of the circle:Area $= \pi r^2 = \frac{22}{7} 	imes (21)^2 = \frac{22}{7} 	imes 21 	imes 21 = 22 	imes 3 	imes 21 = 1386 \, cm^2$.Next,calculate the area of the minor sector:Area of minor sector $= \frac{	heta}{360^{\circ}} 	imes \pi r^2 = \frac{120^{\circ}}{360^{\circ}} 	imes 1386 = \frac{1}{3} 	imes 1386 = 462 \, cm^2$.Then,calculate the area of the major sector:Area of major sector $= 	ext{Total area} - 	ext{Area of minor sector} = 1386 - 462 = 924 \, cm^2$.Finally,find the difference between the areas of the major sector and the minor sector:Difference $= 924 - 462 = 462 \, cm^2$.

Find the difference of the areas of a sector of angle $120^{\circ}$ and its corresponding major sector of a circle of radius $21 \, cm$. (in $cm^2$)

Similar Questions

In a circle with radius $56 \, cm$,find the area of the minor sector,the major sector,and the minor segment corresponding to two radii perpendicular to each other.

The area of a circle is $75.46\, cm^{2}$. Find its circumference. (in $cm$)

In a circle with radius $50 \, cm$,the area of the sector formed by a $20 \, cm$ long arc is $\ldots \ldots \ldots cm^2$.

The radius of a circular ground is $56\,m$. $A$ $7\,m$ wide road runs around its boundary inside the ground. Some region of the road as shown by the shaded part in the diagram is to be repaired. Find the cost of repairing at the rate of ₹ $40/m^2$ (in ₹).

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

Vedclass Test Series

Exam Paper Generator

Online Exam Module