Exemplar Exercise 11.2 (Areas Related to Circles)

Is the area of the circle inscribed in a square of side a cm, πa² cm²? Give reasons for your answer.

Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is 8a cm? Give reasons for your answer.

In Fig 11.3, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

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Is it true to say that 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 2πd cm? Why?

In covering a distance s metres, a circular wheel of radius r metres makes s/2πr 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 is equal to that of an arc of a circle of radius 2 r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other 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) is π b² cm²? Why?

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

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

Is it true to say that area of a square inscribed in a circle of diameter p cm is p² cm²? Why?