Mensuration: Areas Related to Circles

Find the area of the major sector of a circle of radius $7$ cm if the angle of the minor sector is $90^{\circ}$. (Take $\pi = \frac{22}{7}$)

In a circle of radius $21$ cm, an arc subtends an angle of $60^{\circ}$ at the center. Find the length of the arc.

The area of a sector of a circle is $\frac{1}{6}$ to the area of the circle. The degree measure of its minor arc is:

What is the area of a sector of a circle of radius $r$ with central angle $\theta$?

A square $ABCD$ of side $10$ cm is inscribed in a circle. Find the area of one of the four identical segments formed between the sides of the square and the arc of the circle. (Use $\pi = 3.14$)

In the given figure, $O$ is the center of a circle with radius $r = 14$ cm. A sector $OAPB$ subtends an angle of $60^{\circ}$ at the center. Calculate the area of the minor segment $APB$. (Use $\pi = \frac{22}{7}$ and $\sqrt{3} \approx 1.73$)

A square of side $14$ cm is inscribed in a circle. Find the area of the segments of the circle that lie outside the square. (Take $\pi = \frac{22}{7}$)

A park has a circular fountain area with a radius of $14$ m. A design is created in the fountain where a central region is bounded by a chord $AB$ of length $14$ m. The local municipality decides to pave the minor segment formed by this chord with red marble and the rest of the circle with white marble. Calculate the area to be paved with red marble. (Use $\pi = \frac{22}{7}$ and $\sqrt{3} \approx 1.732$)

A square OABC is inscribed in a quadrant OPBQ. If $OA = 20$ cm, find the area of the shaded region (the quadrant excluding the square). (Use $\pi = 3.14$)

In a circle of radius $21$ cm, an arc subtends an angle of $60^\circ$ at the centre. Find the area of the sector formed by this arc. (Use $\pi = \frac{22}{7}$)

Calculate the area of a circle inscribed in a square of side 10 cm. (Take $\pi = 3.14$)

What is the ratio of the area of a circle to the area of a square if their perimeters are equal?

Find the area of a quadrant of a circle whose circumference is 22 cm. (Take $\pi = \frac{22}{7}$)

If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:

The minute hand of a clock is 14 cm long. Find the area swept by the minute hand in 5 minutes.

Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is $60^\circ$. (Take $\pi = \frac{22}{7}$, $\sqrt{3} = 1.73$)

The diameter of the wheels of a car is 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km/h?

In the figure, $OACB$ is a quadrant of a circle with center $O$ and radius 3.5 cm. If $OD = 2 \text{ cm}$, find the area of the shaded region (the quadrant excluding triangle $OBD$). (Use $\pi = \frac{22}{7}$)

Two circular flower beds have been shown on two sides of a square lawn $ABCD$ of side 56 m. If the center of each circular flower bed is the point of intersection $O$ of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors. Find the total length of the silver wire required.