Areas of Sector and Segment of a Circle

A hand fan is made up of cloth fixed in between the metallic wires. It is in the shape of a sector of a circle of radius $21 \mathrm{cm}$ and an angle of $120°$ as shown in the figure. Calculate the area of the cloth used and also find the total length of metallic wire required to make such a fan.

In the figure, $OAPB$ is a quadrant of a circle and $OAP$ is a sector. If $\angle AOP= 30°$ and the area of shaded region is $462 {\mathrm{cm}}^2$, then find the length of the arc $PB$

Find the area of the shaded portion.

Find the measure of the central angle in degrees. (Enter the value to the nearest integer).

Sneha had a rectangular tablecloth with one side measuring 30 cm which she wanted to keep on her circular table of radius 25 cm. After keeping it on the table, she realised that the corners of the tablecloth just touched the edge of the circular table as shown in the figure.

Find the area of the table not covered by the tablecloth. 

(Note: Use $\mathrm{\pi }$ = 3.14.)

Shown below are two paths from Madrid to New York. The dotted line is the shortest distance, approximately $600 \mathrm{km}$, on a $2\mathrm{D}$ map. The other solid circular arc is the shortest distance on a $3\mathrm{D}$ globe and the actual path taken by a flight. The arc subtends an angle of $60°$ at the centre of the circular arc.

What is the actual distance covered by the flight? (Take $\mathrm{\pi }=3.14$, if needed.)

In the figure below, a circle with centre $O$ is inscribed in an equilateral triangle $∆XYZ$. The area of the shaded region of the circle is $2\pi {\mathrm{cm}}^2$.

What is the radius of the circle? Show your steps and give valid reasons.

A $3.5 \mathrm{cm}$ chord subtends an angle of $60°$at the centre of a circle. What is the arc length of the minor sector? Draw a rough figure and show your steps.

If $SQ=QR=RS=SP=PQ, PR=21$ units, what is the area of the black portion.

Earth is excavated to make a railway tunnel. The tunnel is a cylinder of radius $7 \mathrm{m}$ and length $450 \mathrm{m}$. A level surface is laid inside the tunnel to carry the railway lines. Figure given below shows the circular cross-section of the tunnel. The level surface is represented by $AB$, the centre of the circle is $O$ and $\angle AOB=90°$. The space below $AB$ is filled with rubble (debris from the demolition building). A coating is to be done on the surface of the inner curved part. If the area of tunnel to be coated is $a {\mathrm{m}}^2$, then find the value of $a$. [Assume $\mathrm{\pi }=\frac{22}{7}$]

Earth is excavated to make a railway tunnel. The tunnel is a cylinder of radius $7 \mathrm{m}$ and length $450 \mathrm{m}$. A level surface is laid inside the tunnel to carry the railway lines. Figure given below shows the circular cross-section of the tunnel. The level surface is represented by $AB$, the centre of the circle is $O$ and $\angle AOB=90°$. The space below $AB$ is filled with rubble (debris from the demolition building). If the volume of earth removed to make the tunnel is $V {\mathrm{m}}^3$, then find the value of $V$. [Assume $\mathrm{\pi }=\frac{22}{7}$]

Semicircle is a sector or segment. Give reason to your answer.

Belgium is famous for its French fries, which are often served in cones made from newspaper. Rene makes a paper cone from a semicircle cut from a page of his local newspaper. The page measures $410 \mathrm{mm}$ by $315 \mathrm{mm}$.

The circumference of the semi-circle can also be calculated using which of the following formula?

Belgium is famous for its French fries, which are often served in cones made from newspaper. Rene makes a paper cone from a semicircle cut from a page of his local newspaper. The page measures $410 \mathrm{mm}$ by $315 \mathrm{mm}$.

Find the area of the largest cone (to nearest whole number) Rene can make from a page of this newspaper. [Assume $\mathrm{\pi }=\frac{22}{7}$]

Raju and his $3$ friends ordered a pizza one night.

Now, the shop from where they bought this, did not cut it into equal pieces. Raju tried to divide it, but the pieces were not equal.  

As a fun game, he decided to measure the central angles formed and draw the pizza on a piece of paper.

He found that the radius of the pizza is $8 \mathrm{cm}$. The drawing of the pizza came out something like this:

The area of minor sector $\mathrm{HK}$, correct up to $1$ decimal place, assuming $\mathrm{\pi }=\frac{22}{7}$ is

Raju and his $3$ friends ordered a pizza one night.

Now, the shop from where they bought this, did not cut it into equal pieces. Raju tried to divide it, but the pieces were not equal.  

As a fun game, he decided to measure the central angles formed and draw the pizza on a piece of paper.

He found that the radius of the pizza is $8 \mathrm{cm}$. The drawing of the pizza came out something like this:

Find the perimeter of minor sector $KJ$, correct up to $1$ decimal place. [Assume $\mathrm{\pi }=\frac{22}{7}$]

Raju and his $3$ friends ordered a pizza one night.

Now, the shop from where they bought this, did not cut it into equal pieces. Raju tried to divide it, but the pieces were not equal.  

As a fun game, he decided to measure the central angles formed and draw the pizza on a piece of paper.

He found that the radius of the pizza is $8 \mathrm{cm}$. The drawing of the pizza came out something like this:

The perimeter of minor sector $HI$, [assuming $\mathrm{\pi }=\frac{22}{7}$] is

Raju and his $3$ friends ordered a pizza one night.

Now, the shop from where they bought this, did not cut it into equal pieces. Raju tried to divide it, but the pieces were not equal.  

As a fun game, he decided to measure the central angles formed and draw the pizza on a piece of paper.

He found that the radius of the pizza is $8 \mathrm{cm}$. The drawing of the pizza came out something like this:

The length of minor arc $HI$ [to the nearest whole number, assuming $\mathrm{\pi }=\frac{22}{7}$] will be

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