Worked out Examples
example.1
What is
the area of the triangle with sides 12 cm, 13 cm and 15 cm?
Solution
When the
three sides a, b and c of a triangle are given,
then its area = 
Where s = 
= 20 cm
Area = 
= 20
cm2
example.2
The area of the base of a right circular cone
is 154 cm2 and its vertical height is 24 cm. What is its curved
surface area? .
Solution
Area of
the base = pr2 = 154 ⇒ r = 7 cm.
Slant height = 
= 
= 25 cm
\ Curved surface area = prl = 
x 7 x 25
= 550 cm2.
example.3
What is the area of a regular hexagon whose
side measures 4 cm?
Solution
The hexagon can be divided into six
equilateral triangles of equal areas. Area of the hexagon = 6 x 
x 4 x 4 =
24
cm2
example.4
The radius of the base and the height of a
cylinder are 14 cm and 20 cm respectively. What is the volume of the cylinder? .
Solution
Volume of
a cylinder = pr27
= 22/7 x 14 x 14 x 20 = 12320 cm3
example.5
A sphere of radius 7 cm is cut into two equal
halves. What is the volume of each of the halves? .
Solution
Each half is a hemisphere of radius 7 cm. .
\ Volume of each of the halves
= 
pr3 = 
(7)3
= 
= 
= 718cu.cm
