Areas Related to Circles — Class 10 Mathematics (Standard) PYQs

The area of a sector of a circle of radius $10\text{cm}$ is $\frac{55}{3}{\text{cm}}^2$. The value of central angle is

A circle of diameter $20\text{cm}$ is equally divided into five sectors. Find the area and perimeter of one of the sectors.

An arc of length $2.2\text{cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{cm}$. The value of $\theta$ is

A chord of a circle, of radius $14\text{cm}$, subtends an angle of $60^{\circ }$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

If a sector of a circle has an area of $40\pi$ sq. units and a central angle of $72^{\circ }$, the radius of the circle is :

A piece of wire $20\text{cm}$ long is bent into the form of an arc of a circle of radius $\frac{60}{\pi }\text{cm}$. The angle subtended by the arc at the centre of the circle is :

Case Study - 1

An arc of a circle is of length $5\pi \text{cm}$ and the sector it bounds has an area of $20\pi {\text{cm}}^2$. Its radius is :

If a large circular pizza is divided into $5$ equal sectors, then the central angle of each sector will be :

(a) In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $\angle AOB=90^{\circ }$. If $AO=OB=42\text{cm}$, then find the perimeter of the top of the table.
OR
(b) In the given figure, three sectors of a circle of radius $5\text{cm}$, making angles $35^{\circ },50^{\circ }$ and $95^{\circ }$ at the centre are shaded. Find the area of the shaded region. [Use $\pi =\frac{22}{7}$]