Curved Surface Area Examples

Here on this page "curved surface area examples" we are going to have some practice problems on curved surface-area for some particular solids.

Example 1:

A circus tent is in the form of a cylinder with a height of 3 m and conical above it. If the base radius is 52.5 m and the slant height of the cone is 53 m, find the canvas needed to make the tent.

solution:

Cylindrical part:

The radius of the cylindrical part (r) = 52.5 m

Height of the cylindrical part(h) = 3 m

Curved surface-area of the cylindrical part = 2πrh
                                                                                = 2π(52.5)(3)
                                                                                = 315 π m²

Conical part:
The radius of the conical part = 52.5 m
Slant height of the conical part = 53 m
Curved Surface-area of the conical part = πrl
                                                                           = π(52.5)(53)
                                                                           = (2782.5)π

Area of the canvas required:
Area of the canvas required = CSA of the cylindrical part +

                                                          CSA of the conical part
                                                    = 315π + (2782.5)π
                                                   = (3097.5)π m²

Hence, Area of the canvas required =  (3097.5)π m²


Example 2

A vessel is in the form of hollow cylinder which has been surmounted on a hemispherical bowl.The diameter of a hemisphere is 14cm and the total height of a vessel is 13cm. Find the required curved surface area of the vessel.

Solution:

Diameter of the hemisphere = 14 cm
Radius of the hemisphere = 14/2 = 7 cm
Radius of the cylinder = radius of the hemisphere = 7 cm
Total height of the vessel = 14 cm
Total height of the vessel = height of the cylinder + radius of the hemisphere

13 = height of the cylinder + 7

Height of the cylinder = 13 - 7 = 6 cm

Curved Surface Area of the vessel = CSA of the cylinder + CSA of the hemisphere
                                                                = 2πrh + 2πr²
Here r = 7 and h = 6
                                        = 2π(7)(6) + 2π (7)²
                                       = 84π + 98π
                                       =182π
Hence, the Curved Surface Area of the Vessel = 182 π cm²

Student who are practicing problems on curved surface area can go through the steps of the above problems on curved surface area examples to have better understanding. curved surface area examples

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