A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, find the total area of the canvas required.
Given: diameter of base of cone and the cylinder = 105 m
∴ Radius of cylinder = rcl = 105/2 = 51 m
Radius of cone = rco = 105/2 = 51 m
Height of cylinder = h = 4 m
Slant height of cone = l = 40 m
Formula: Surface area of cylinder = 2πrclh + 2πrcl2
Surface area of cone = πrco2 + πrcol
Since we don’t require canvas for the top surface and bottom surface of cylinder and also for the base of cone we should subtract those areas from the surface area
Area of upper and lower surfaces of cylinder = 2πrcl2
∴ Area of canvas required for cylinder = 2πrclh + 2πrcl2 - 2πrcl2
= 2πrclh
= 2 × 3.14 × 51 × 4
= 1281.12 m2
Area of base of cone = πrco2
∴ area of canvas required for cone = πrco2 + πrcol - πrco2
= πrcol
= 3.14 × 51 × 40
= 6405.6 m2
Total area of canvas required = Area of canvas required for cylinder + area of canvas
required for cone
= 1281.12 + 6405.6
= 7686.72 m2
∴ Total area of canvas required = 7686.72 m2