TOTAL SURFACE AREA EXAMPLE

Total surface area examples :

Here we are going to see some example problems to understand how to find the total surface area of the any shapes.

Example 1 :

A toy is in the form of right circular cylinder with a hemisphere at the one end and a cone at the other end.The base radius  measures 3.5 cm , height of the cylindrical portion is 10 cm. and conical part measures 12 cm.Find the total surface-area of the toy(use π = 3.14)

Solution : Radius of the hemisphere = 3.5 cm

C.S.A of the hemisphere = 2πr²square units

=  2(3.5)²π

=  (24.5)π cm²

Radius of the Cylinder r = 3.5 cm

Height of the Cylinder h = 10 cm

C.S.A of the Cylinder = 2πrh square units

=  2 π  x .5 x 10

=  70π cm²

Radius of the cone r= 3.5 cm

Height of the cone h = 12 cm

Slant height of the cone l = √(r² + h²)

l = √(3.5² + 12²)

l = √(12.25+144)

l = √(156.25)

l = 12.5 cm

C.S.A of the Cone = πrl square units

=  π(3.5)(12.5)

=  (43.75)π cm²

T.S.A of the toy  =  CSA of hemisphere +                                                 (CSA of cylinder) + (CSA of cone)

=  (24.5 π) + (70 π) + (43.75 π)

=  138.25  x 3.14

Hence, total surface area of the toy  =  434.11 cm²

Example 2 :

Find the total surface area of cylinder whose height is 8 cm and radius is 4 cm.

Solution : Radius of the Cylinder = 4 cm

Height of the cylinder = 8 cm

Required total surface area of the cylinder = 2πr(h+r)

=  2 π (4) (8+4)

=  2 π (4) (12)

=  96 π

Hence, total surface area of the Cylinder = 96π cm²

Example 3

Find the total surface area of cylinder whose height is 16 cm and radius is 7 cm.

Solution:

Radius of the Cylinder = 7 cm

Height of the cylinder = 16 cm

Required Total surface area of the cylinder  =  2πr(h+r)

=  2 (22/7) (7) (16+7)

=  2 (22) (23)

= 1012 cm²

Hence, Total surface area of the Cylinder = 1012 cm²

Student who are practicing questions on total surface area can go through the steps of the above questions on total surface area to have better understanding.

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