Q. 35.0( 4 Votes )

Answer :

Given: diameter of base of cone and the cylinder = 105 m

∴ Radius of cylinder = r_{cl} = 105/2 = 51 m

Radius of cone = r_{co} = 105/2 = 51 m

Height of cylinder = h = 4 m

Slant height of cone = l = 40 m

Formula: Surface area of cylinder = 2πr_{cl}h + 2πr_{cl}^{2}

Surface area of cone = πr_{co}^{2} + πr_{co}l

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 = 2πr_{cl}^{2}

∴ Area of canvas required for cylinder = 2πr_{cl}h + 2πr_{cl}^{2} - 2πr_{cl}^{2}

= 2πr_{cl}h

= 2 × 3.14 × 51 × 4

= 1281.12 m^{2}

Area of base of cone = πr_{co}^{2}

∴ area of canvas required for cone = πr_{co}^{2} + πr_{co}l - πr_{co}^{2}

= πr_{co}l

= 3.14 × 51 × 40

= 6405.6 m^{2}

Total area of canvas required = Area of canvas required for cylinder + area of canvas

required for cone

= 1281.12 + 6405.6

= 7686.72 m^{2}

∴ Total area of canvas required = 7686.72 m^{2}

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