The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in Fig. 21.11. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of a radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm^{2} and black paint cost 5 paise per cm^{2}.

Surface area of a sphere = 4πr^{2}

Curved surface area of a cylinder = 2πrh

Base area of a cylinder = πr^{2}

Given, front compound wall of a house is decorated by wooden spheres of diameter 21 cm placed on small supports.

Each support is a cylinder of a radius 1.5 cm and height 7 cm and is to be painted black

Thus, the surface area of the sphere would be reduced by the cylindrical supports base.

Total surface area of the spherers = 8 × (4 × (22/7) × (21/2)^{2} – (22/7) × 1.5^{2}) = 11031.43 cm^{2}

Total curved surface area of the spheres = 8 × 2 × (22/7) × 1.5 × 7 = 528 cm^{2}

Silver paint costs 25 paise per cm^{2} and black paint cost 5 paise per cm^{2}

Total cost of painting = 11031.43 × 0.25 + 528 × 0.05 = Rs. 2784.26

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