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Question -

The front compound wall of a house isdecorated by wooden spheres of diameter 21 cm, placed on small supports asshown in the given figure. Eight such spheres are used for this purpose, andare to be painted silver. Each support is a cylinder of radius 1.5 cm andheight 7 cm and is to be painted black. Find the cost of paint required ifsilver paint costs 25 paise per cm2 andblack paint costs 5 paise per cm2.



Answer -

Radius (r)of wooden sphere = 

Surface area of wooden sphere = 4πr2

Radius (r1) ofthe circular end of cylindrical support = 1.5 cm

Height (h)of cylindrical support = 7 cm

CSA of cylindrical support = 2πrh

Area of the circular end ofcylindrical support = πr2 

= 7.07 cm2

Area to be painted silver = [8 × (1386 − 7.07)] cm2

= (8 × 1378.93) cm2 =11031.44 cm2

Cost forpainting with silver colour = Rs (11031.44 × 0.25) = Rs 2757.86

Area to be painted black = (8 × 66) cm= 528 cm2

Cost forpainting with black colour = Rs (528 × 0.05) = Rs 26.40

Total costin painting = Rs (2757.86 + 26.40)

= Rs2784.26

Therefore, it will cost Rs 2784.26 in painting in such away.

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