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)
Radius of the hemisphere = 3.5 cm
C.S.A of the hemisphere = 2πr²square units
= (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
= (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.
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
Find the total surface area of cylinder whose height is 16 cm and radius is 7 cm.
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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