NCERT Solutions for Chapter: Areas Related to Circles, Exercise 1: Exercise

Ramit drew two circles of different radii. Each of them had an arc that subtended an equal angle at the centre.

He said, "Both arcs are of the same length".
i) Is Ramit right?

ii) If both radii and angles subtended by the two arcs are different, can the arc lengths be the same?

A circle has radius 5 cm. Three chords of lengths 6 cm, 8 cm and 10 cm are drawn.

Which chord subtends the largest angle on its minor arc?

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 the trophy shield Rishika received on winning an inter school tennis tournament.

The trophy is made of a glass sector DOC supported by identical wooden right triangles, $∆\mathrm{DAO} \mathrm{and} ∆\mathrm{COB}.$ AO = 7 cm and $\mathrm{AO}:\mathrm{DA} = 1:\sqrt{3}.$

Find the area of:

i) the glass sector correct to 2 decimal places.

ii) the wooden triangles correct to 2 decimal places.

(Note: Take $\mathrm{\pi }$ as $\frac{22}{7}$ and $\sqrt{3}$ as 1.73.)

At a certain roundabout, the radius of the circular region is $50 \mathrm{ft}$. The circular region includes a $2 \mathrm{ft}$ wide circular concrete footpath and a flowering bed. The flowering bed is divided into three parts using two dividers of length $48\sqrt{3} \mathrm{ft}$ each as shown below.

Find the area of regions $\left(\mathrm{I}+\mathrm{III}\right)$, in terms of $\mathrm{\pi }$.

Sprinklers are crop irrigation equipment which rotate around a center and spay water on the crops in the circular region. Two such high power sprinklers, occupying negligible area are installed in a straight line in a field such that they spray water on a common area. Shown below are the side and top views where points A and B are the sprinklers.

Both the sprinklers spray over an equal area. It is given that, $\mathrm{CD} = 400 \mathrm{m}$ and $\angle \mathrm{CAD} = \angle \mathrm{CBD} = 90°.$

i) Find the radius of the circular region sprayed by the sprinkler.
ii) Find the area of the overlapping region.