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.
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
= 315 π m²
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.
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
Hence, the Curved Surface Area of the Vessel = 182 π cm²
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