In a circle with radius 20 ,cm,the measures o | vedclass

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

Question

(C) The area of a sector of a circle with radius $r$ and central angle $	heta$ is given by the formula: $A = \frac{	heta}{360^{\circ}} 	imes \pi r^

Vedclass · Accepted Answer

$1: 6$

Vedclass · Answer

(C) The area of a sector of a circle with radius $r$ and central angle $	heta$ is given by the formula: $A = \frac{	heta}{360^{\circ}} 	imes \pi r^2$.Let the two sectors have angles $	heta_1 = 15^{\circ}$ and $	heta_2 = 90^{\circ}$.The ratio of the areas of the two sectors is:$\frac{A_1}{A_2} = \frac{\frac{	heta_1}{360^{\circ}} 	imes \pi r^2}{\frac{	heta_2}{360^{\circ}} 	imes \pi r^2} = \frac{	heta_1}{	heta_2}$.Substituting the given values:$\frac{A_1}{A_2} = \frac{15^{\circ}}{90^{\circ}} = \frac{1}{6}$.Thus,the ratio of the areas of the sectors is $1: 6$.

In a circle with radius $20 \,cm$,the measures of the angle subtended at the centre for two distinct sectors are $15^{\circ}$ and $90^{\circ}$. Then,the ratio of the areas of those sectors is $\ldots \ldots \ldots$.

Similar Questions

$A$ piece of wire $20 \,cm$ long is bent into the form of an arc of a circle subtending an angle of $60^{\circ}$ at its centre. Find the radius of the circle. (in $cm$)

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

In a circle with radius $8.4 \, cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to this arc.

In a circle with radius $10 \, cm$,the area of a minor sector is $75 \, cm^2$. Then,the length of the arc of that sector is $\ldots \, cm$.

The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

Vedclass Test Series

Exam Paper Generator

Online Exam Module