In a circle with radius r,the area of a secto | vedclass

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

Question

(D) The area of a sector of a circle is given by the formula $A = \frac{	heta}{360^\circ} 	imes \pi r^2$,where $	heta$ is the central angle in degr

Vedclass · Accepted Answer

$\frac{1}{2} r l$

Vedclass · Answer

(D) The area of a sector of a circle is given by the formula $A = \frac{	heta}{360^\circ} 	imes \pi r^2$,where $	heta$ is the central angle in degrees.We know that the length of an arc $l$ is given by $l = \frac{	heta}{360^\circ} 	imes 2 \pi r$.From this,we can express the term $\frac{	heta}{360^\circ}$ as $\frac{l}{2 \pi r}$.Substituting this into the area formula: $A = \left( \frac{l}{2 \pi r} ight) 	imes \pi r^2$.Simplifying the expression: $A = \frac{l 	imes \pi r^2}{2 \pi r} = \frac{1}{2} r l$.

In a circle with radius $r$,the area of a sector formed by an arc of length $l$ is.........

Similar Questions

Find the area of the sector of a circle of radius $5\, cm$,if the corresponding arc length is $3.5\, cm$. (in $cm^2$)

The side length of square $ABCD$ shown in the diagram is $42 \ cm$. The shaded design is formed by drawing semicircles on all the sides of the square. Find the area of the shaded design in $cm^2$.

Will it be true to say that the perimeter of a square circumscribing a circle of radius $a \, cm$ is $8 a \, cm$? Give reasons for your answer.

From a circular metallic sheet with radius $21\, cm$,a regular hexagon of side $21\, cm$ is cut off. Find the area of the remaining sheet. $(\sqrt{3} = 1.73)$ (in $cm^2$)

As shown in the diagram,$\triangle ABC$ is an equilateral triangle in which $BC = 70 \, cm$ and $P$ and $R$ are midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. $\widehat{PQR}$ is an arc of $\odot(A, AP)$. Find the area of the shaded region. $(\sqrt{3} = 1.73)$ (in $cm^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module