The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in fig. Eight such spheres are used forth is purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2.
Diameter of wooden sphere = 21 cm
Radius of wooden sphere, r = diameter/ 2
= (21/2) cm = 10.5 cm
Surface area of wooden sphere = 4πr2
= 4 × (22/7) × (10.5)2
= 1386
Surface area is 1386 cm3
Radius of the circular end of cylindrical support = 1.5 cm
Height of cylindrical support = 7 cm
Curved surface area = 2πrh
= 2 × (22/7) × 1.5 × 7 = 66
So, CSA is 66 cm2
Area of the circular end of cylindrical support = πr2
= (22/7) × 1.52
= 7.07
Area of the circular end is 7.07 cm2
Area to be painted silver = [8 × (1386 - 7.07)]
= 8 × 1378.93 = 11031.44
Area to be painted is 11031.44 cm2
Cost for painting with silver colour
= Rs(11031.44 × 0.25)
= Rs 2757.86
Area to be painted black = (8 × 66) cm2
= 528 cm2
Cost for painting with black colour = Rs (528 × 0.05)
= Rs 26.40
Therefore, the total painting cost is:
= Rs(2757.86 + 26.40)
= Rs 2784.26