NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles

Exercise 11.2

Is the area of the circle inscribed in a square of side a cm equal to \(\pi a^2\) cm²?

Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is \(8a\) cm?

In Fig. 11.3, a square is inscribed in a circle of diameter \(d\) and another square circumscribes the circle. Is the area of the outer square four times the area of the inner square?

Is it true that the area of a segment of a circle is less than the area of its corresponding sector? Why?

Is it true that the distance travelled by a circular wheel of diameter \(d\) cm in one revolution is \(2\pi d\) cm? Why?

In covering a distance \(s\) metres, a circular wheel of radius \(r\) metres makes \(\dfrac{s}{2\pi r}\) revolutions. Is this statement true? Why?

The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

If the length of an arc of a circle of radius \(r\) equals that of an arc of a circle of radius \(2r\), then the angle of the sector of the first circle is double the angle of the sector of the second circle. Is this statement false? Why?

The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

Is the area of the largest circle that can be drawn inside a rectangle of length \(a\) cm and breadth \(b\) cm (\(a>b\)) equal to \(\pi b^2\) cm²? Why?

Circumferences of two circles are equal. Is it necessary that their areas are equal? Why?

Areas of two circles are equal. Is it necessary that their circumferences are equal? Why?

Is it true to say that the area of a square inscribed in a circle of diameter \(p\) cm is \(p^2\) cm²? Why?