A cow is tied at one of the corners of a square shed. The length of the rope is 22 m. The cow can only eat the grass outside the shed as shown below.

What is the area that the cow can graze on? 

(Note: Give the answer in terms of $\mathrm{\pi }$)

Avikant bought a pair of glasses with wiper blades. He was curious to know the area being cleaned by each of the wiper blades. With the help of a ruler and a protractor, he found the length of each blade as 3 cm and the angle swept as 60°.

i) Find the area that each wiper cleans in one swipe, in terms of $\mathrm{\pi }$.
ii) If the diameter of each circular glass is 5 cm, what percent of the area of the glass will be cleaned by the blade in one swipe?

The figure below is a part of a circle with centre O. Its area is $\frac{1250\mathrm{\pi }}{9}{\mathrm{cm}}^2$ and the 10 sectors are identical.

Find the value of $\beta$ in degrees.

Shown below is a circle with centre O. Chord MN subtends an angle at centre O.

Which of these is true for the above circle?

$$\begin{gathered} 1. \frac{\mathrm{x}}{{360}^{\circ }}=\frac{\text{length of arc MPN}}{\text{circumference of the circle}} \\ 2. \frac{\mathrm{x}}{{360}^{\circ }}=\frac{\text{minor sector area}}{\text{area of the circle}} \end{gathered}$$

Shown below is a circle with centre O. The shaded sector has an angle of $280°$ and area $\mathrm{A} {\mathrm{cm}}^2$.

Which of these is the area of unshaded sector?

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 the biggest share of pizza (correct to two decimal places) will be [assume $\mathrm{\pi }=\frac{22}{7}$]

In a fair, a giant wheel was fixed. The giant wheel is in the shape of a circle divided into $12$ equal sectors as shown in the diagram below.

The highest point of the wheel is $150 \mathrm{m}$ above the ground level and the boarding platform of the wheel is $10 \mathrm{m}$ above the ground level. Based on the given information, answer the following question by choosing the correct option from the given four options in the question:

The perimeter of each sector of the circle is

Fibonacci's sequence is a pattern in which each number is obtained by adding the previous two numbers (except the first $2$ numbers).

The pattern is $0, 1, 1, 2, 3, 5, 8, 13...$

Shown below is a representation of the first few terms of the Fibonacci sequence in a unit square grid. The terms represent the side lengths of the squares.

What is the area of the shaded sector?