CLASS-9
CIRCUMFERENCE & AREA OF SEMI-CIRCLE
CIRCUMFERENCE & AREA OF SEMI CIRCLE -
For a semi circle of radius = r units, we have –
1
(i) Area of the semi-circle = ------ πr² sq.units
2
(ii) Perimeter of a semi-circle = (πr + 2r) units
Example.) The perimeter of a semi circular protractor is 32.4. calculate the following
i) The radius of the protractor in cm
ii) The area of the protractor in cm
ii) The area of the protractor in cm²
Ans.) Let the radius of the protractor be r cm
As per the formulae, its perimeter = (πr + 2r) cm
According to the condition, πr + 2r = 32.4
Or, r(π + 2) = 32.4
22
Or,
r (------ + 2) = 32.4
7
36
Or, ------ r = 32.4
7
32.4 X 7
Or, r = ------------ = 6.3 cm ................(i) (Ans.)
36
Area of the protractor = πr²/2
1 22
= ------- X ------- X 6.3 X 6.3
2 7
= 62.37 cm²
So, area of protractor 62.37 cm² (Ans.)