AREAS RELATED TO CIRCLES - True/False

The circumference of a circle of radius \(r\) is given by \(2\pi r.\)

The area of a circle becomes four times if its radius is doubled.

The area of a circle is directly proportional to its radius.

The length of an arc of a sector of angle \(\theta\) (in degrees) in a circle of radius \(r\) is \(\dfrac{\theta}{360^\circ} \times 2\pi r\)

The area of a sector of angle \(\theta\) (in degrees) in a circle of radius \(r\) is \(\dfrac{\theta}{360^\circ} \times \pi r^2\)

A segment of a circle is the region between two radii and the corresponding arc.

The area of a segment of a circle is obtained by subtracting the area of the corresponding triangle from the area of the corresponding sector.

The area of a ring (or circular path) with outer radius \(R\) and inner radius \(r\) is \(\pi(R^2 - r^2)\)

If two circles have equal circumferences, then their areas must be different.

If the diameter of a circle is 14 cm, then its radius is 7 cm.

The circumference of a circle is numerically equal to the area of the circle for radius \(r=2r\)

In the formulae of this chapter, \(\pi\) is often taken as \(\dfrac{22}{7}\) or 3.14 for numerical calculations.

The area of a semicircle of radius rrr is \(\pi r^2\)

The perimeter of a semicircle of radius \(r\) (including diameter) is \(\pi r + 2r\)

The sum of the areas of the major segment and the minor segment of a circle equals the area of the circle.

In this chapter, many problems involve finding areas of figures formed by combinations of circles with rectangles, triangles or squares.

The length of the arc of a full circle of radius \(r\) is \(\pi r\)

If the radius of a circle is tripled, its area becomes nine times.

A sector with central angle \(180^\circ\) is called a semicircular region.

A quadrant is a sector of a circle whose central angle is\(60^\circ\)

The unit of circumference of a circle is always in square units.

The unit of area of a circle is always in square units.

For a fixed radius, the area of a sector increases as its central angle increases.

In problems on circular paths around a circular field, the width of the path is the difference between the outer and inner radii.

Every chord of a circle divides it into two sectors.