Notes On Circles - CBSE Class 7 Maths
Circle A circle is defined as a collection of points on a plane that are at an equal distance from a fixed point on the plane. The fixed point is called the centre of the circle. Any line segment that passes through the centre of a circle and whose end points are on the circle is called its diameter. Any line segment from the centre of the circle to its circumference is called the radius of the circle. The diameter of a circle is two times the radius. Circumference of a circle The distance around a circular region is known as its circumference. Ratio of circumference and diameter of a circle is denoted by the Greek symbol π. π is an irrational number, whose value is approximately equal to $\frac{\text{22}}{\text{7}}$ or 3.14 Circumference of a circle = 2πr, where r is the radius of the circle  or Circumference of a circle = πd, where d is the diameter of the circle.  Circumference = Diameter x 3.14 Area of a circle The area of a circle is the region enclosed in the circle. The area of a circle can be calculated by using the formula is πr2, if radius r is given; $\frac{{\pi \text{d}}^{\text{2}}}{\text{4}}$, if diameter d is given;  $\frac{{\text{C}}^{\text{2}}}{\text{4}\pi }$, if circumference C is given. Concentric circles Circles with the same centre but different radii are called concentric circles. Area between two concentric circles  = Area of outer circle – Area of inner circle. Conversion of units To convert from a unit of area to its smaller unit of area, we multiply. To convert from a unit of area to a larger unit of area, we divide. 1 cm = 10 mm 1 m = 100 cm 1 km = 1000 m 1 cm2 = 100 mm2 1 m2 = 10000 cm2 1 km2 = 1000000 m2 1 hectare = 10000 m2

#### Summary

Circle A circle is defined as a collection of points on a plane that are at an equal distance from a fixed point on the plane. The fixed point is called the centre of the circle. Any line segment that passes through the centre of a circle and whose end points are on the circle is called its diameter. Any line segment from the centre of the circle to its circumference is called the radius of the circle. The diameter of a circle is two times the radius. Circumference of a circle The distance around a circular region is known as its circumference. Ratio of circumference and diameter of a circle is denoted by the Greek symbol π. π is an irrational number, whose value is approximately equal to $\frac{\text{22}}{\text{7}}$ or 3.14 Circumference of a circle = 2πr, where r is the radius of the circle  or Circumference of a circle = πd, where d is the diameter of the circle.  Circumference = Diameter x 3.14 Area of a circle The area of a circle is the region enclosed in the circle. The area of a circle can be calculated by using the formula is πr2, if radius r is given; $\frac{{\pi \text{d}}^{\text{2}}}{\text{4}}$, if diameter d is given;  $\frac{{\text{C}}^{\text{2}}}{\text{4}\pi }$, if circumference C is given. Concentric circles Circles with the same centre but different radii are called concentric circles. Area between two concentric circles  = Area of outer circle – Area of inner circle. Conversion of units To convert from a unit of area to its smaller unit of area, we multiply. To convert from a unit of area to a larger unit of area, we divide. 1 cm = 10 mm 1 m = 100 cm 1 km = 1000 m 1 cm2 = 100 mm2 1 m2 = 10000 cm2 1 km2 = 1000000 m2 1 hectare = 10000 m2

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