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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.

A

Rs. 1784.26

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B

Rs. 2734.26

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C

Rs. 6784.26

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D

Rs. 2784.26

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Solution

## The correct option is D Rs. 2784.26 Radius (r) of wooden sphere=(212)cm=10.5 cm Surface area of the wooden sphere =4πr2 =[4×227×(10.5)2]cm2=1386 cm2 Radius (r1)of the circular end of cylindrical support =1.5 cm Height (h) of the cylindrical support = 7 cm CSA of the cylindrical support =2πrh =[2×227×(1.5)×7]cm2=66 cm2 Area of the circular end of cylindrical support =πr2 =[2×227×(1.5)2]cm2=7.07 cm2 Area to be painted silver =[8×(1386−7.07)]cm2=(8×1378.93) cm2=11031.44 cm2 Cost fo ther painting with silver colour =Rs. (11031.44×0.25)=Rs. 2757.86 Area to be painted black =(8×66) cm2=528 cm2 Cost for the 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 for painting in such a way.

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