Question
The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of 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 costs 5 paise per cm2.
Solution
Radius (r) of wooden sphere = (21/2)cm = 10.5cm
Surface area of wooden sphere = 4πr2
`=[4xx22/7xx(10.5)^2]cm^2 = 1386cm^2`
Radius (r1) of the circular end of cylindrical support = 1.5 cm
Height (h) of cylindrical support = 7 cm
CSA of cylindrical support = 2πrh
`=[2xx22/7xx(1.5)xx7]cm^2 = 66cm^2`
Area of the circular end of cylindrical support = πr2
`=[22/7xx(1.5)^2]cm^2=7.07cm^2`
Area to be painted silver = [8 × (1386 − 7.07)] cm2
= (8 × 1378.93) cm2 = 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
Total cost in painting = Rs (2757.86 + 26.40)
= Rs 2784.26
Therefore, it will cost Rs 2784.26 in painting in such a way.
