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 cm2 and black paint cost 5 paise per cm2.
Surface area of a sphere = 4πr2
Curved surface area of a cylinder = 2πrh
Base area of a cylinder = πr2
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) × 1.52) = 11031.43 cm2
Total curved surface area of the spheres = 8 × 2 × (22/7) × 1.5 × 7 = 528 cm2
Silver paint costs 25 paise per cm2 and black paint cost 5 paise per cm2
Total cost of painting = 11031.43 × 0.25 + 528 × 0.05 = Rs. 2784.26