Areas of Sector and Segment of a Circle

The area of the minor segment of a circle is $41$ square units and the area of major segment of a circle is $57$ square units. Find the area of the circle

The area of the minor segment of a circle is $30$ square units and the area of major segment of a circle is $57$ square units. Find the area of the circle

The area of the minor segment of a circle is $25$ square units and the area of major segment of a circle is $27$ square units. Find the area of the circle

The area of the minor segment of a circle is $50$ square units and the area of major segment of a circle is $100$ square units. Find the area of the circle

If the area of the minor segment of a circle of radius $14 \mathrm{cm}$, when its central angle is $60°$ is $k {\mathrm{cm}}^2$, then find the value of $k$, rounded off to one decimal place, considering $\mathrm{\pi }=\frac{22}{7}$ and $\sqrt{3}=1.732$.

The minute-hand of a clock is $15 \mathrm{cm}$ long. Calculate the area swept by it in $20$ minutes. If the area is $k {\mathrm{cm}}^2$ then, write the value of $k$ as final answer. [Take $\pi =3.14$]

A round table cover has six equal designs as shown in the given figure. If the radius of the cover is $35 \mathrm{cm}$, then find the total area(approximately up to two decimal places) of the design in square centimeters. [Use $\sqrt{3}=1.732$ and $\pi =3.14$].

If the total area of the design is $\mathrm{k} {\mathrm{cm}}^2$, then write the value of $\mathrm{k}$ as final answer.

If the length of an arc of sector of a circle is $20 \mathrm{cm}$ and if radius is $7 \mathrm{cm}$, find the area of the sector in ${\mathrm{cm}}^2$.

$ABCD$ is a rectangle of length $20 \mathrm{cm}$ and breadth $10 \mathrm{cm}.$ $OAPB$ is a sector of a circle of radius $10\sqrt{2} \mathrm{cm}.$ Calculate the area of the shaded region in square centimetre. [take $\pi =3.14]$

The radius of a circle is $9 \mathrm{cm}$ and the central angle is $70°$. Find the area of the minor sector of the circle in square centimetre. (Take $\pi =\frac{22}{7}$)

In the given figure, $ABCD$ is a rectangle, in which side $AB=10 \mathrm{cm}$ and $BC=7 \mathrm{cm}$. From each vertex of the rectangle, four circles with radii $3.5 \mathrm{cm}$ each are drawn. If the area of the shaded portion is $k {\mathrm{cm}}^2$, find the value of $k$. (Take $\pi =\frac{22}{7}$)

Shown below (left) is a piece of tin in the shape of a sector of angle $216°$ and radius of $25 \mathrm{cm}$. The tin is folded into a cone as shown below.

What is the height of the cone?

Shown below (left) is a piece of tin in the shape of a sector of angle ${216}^{°}$ and radius of $25 \mathrm{cm}$. The tin is folded into a cone as shown below.

Which of the following is the base radius of the cone?

The perimeter of sector of a circle of radius $R=2 \mathrm{units}$ with central angle $\theta =90°$ is $($_____$+\mathrm{\pi })$ units.

In the given figure, $O$ is the centre of the circle. If $\angle AOB=90°$ and $OA=3 \mathrm{cm}$, then the area of the shaded region is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$(in two decimal places).

The minute hand of a clock is $5 \mathrm{cm}$ long. The area of the sector (in two decimal places) formed by this hand in $7$ minutes is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$.

The circumference of a circle is $22 \mathrm{cm}$. The area of its one quadrant is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$. (in three decimal places).

The radius of a circle is $3.5 \mathrm{cm}$ and the angle subtended by a chord at the centre is $90°$. The area of the minor segment of the circle (in one decimal place) formed by this chord is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$. (Take $\pi =\frac{22}{7}$).

The length of the minute hand of a clock is $10.5 \mathrm{cm}$. The area of the sector(to two decimal places) swept by the minute hand in $10$ minutes is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$ (Take $\pi =\frac{22}{7}$)

An arc of a circle with radius $21 \mathrm{cm}$ subtends an angle of $60°$at the centre. The area of the sector formed by corresponding chord in two decimal places is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of$\mathrm{k}$.  (Take $\pi =\frac{22}{7}$ and $\sqrt{3}=1.73$)