Total Surface Area Example

Total Surface Area examples is containing some practice questions on total surface area for some particular solids.

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
Curved Surface-area(CSA) 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
Curved Surface-Area(CSA) of the Cylinder = 2πrh square units.
                                                                              = 2 π  x 3.5 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
Curved Surface-Area(CSA) of the Cone = πrl square units
                                                                        = π(3.5)(12.5)
                                                                        = (43.75)π cm²
Total Surface-Area of the Toy = CSA of the hemisphere +

                                                 (CSA of the Cylinder) + (CSA of the 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.    total surface area example total surface area example


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