In our daily life, we come across many circular objects like coins, cakes, plates, wheels, wheelbarrows, brooches, bangles, flower beds, etc. So, the problem of finding perimeters and the area of plane circular figures have great practical importance.
Review of Perimeter And Area of A Circle:
Circle: A circle is a closed
curve consisting of a set of all those points of the plane which are at a
constant distance from a fixed point in the plane.
Centre: The fixed point is called its centre.
Radius: The constant distance is
called its radius. It is the line segment joining any point on the boundary
(circumference) to the centre.
Circumference:
The boundary (or perimeter) of a circle
is called its circumference.
The circumference of a circle bears a constant ratio with its diameter. this
constant ratio is denoted by Pi (p),
a Greek letter.
In
other words,
Or, Circumference =
(where r is the radius of the circle)
Area of Circle:
Cut a circle of radius r into a number of sectors and rearrange them as
shown in the figure.
Let us see this with an applet and learn how exactly area of a circle comes in.
The sector can be rearranged together in nearly a rectangle of length and breadth r.
Area Enclosed Between Two Concentric Circles:
The fig. bounded by two concentric circles is called the annulus.
If the radii of the outer and inner circles are R and r, respectively,
then
The area is enclosed between two concentric circles.
Some useful points about Circles:
(i) If two
circles touch externally, then the distance between their centres is equal to
the sum of their radii (fig.)
(ii) If two
circles touch internally, then the distance between their centres is equal to
the difference of their radii
(iii) Distance
covered by a moving wheel in one revolution is equal to the circumference of
the wheel.
(iv) Number of revolutions made by a circular wheel =
.