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# The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in 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 $$cm^2$$ and black paint costs 5 paise per $$cm^2$$.

Diameter of wooden sphere = 21 cm
Radius of wooden sphere, (r)
= $$\frac{diameter}{2}$$
= ($$\frac{21}{2}$$) cm
= 10.5 cm

Surface area of a wooden sphere
$$= 4\pi r^2$$
$$= 4×(\frac{22}{7} )×(10.5)^2 = 1386$$$$cm^2$$

Radius of the circular end of cylindrical support = 1.5 cm
Height of cylindrical support = 7 cm

Curved surface area of one cylindrical support
= 2$$\pi$$rh
= 2×($$\frac{22}{7}$$)×1.5×7
= 66 $$cm^2$$
Now,
Area of the circular end of cylindrical support
= $$\pi r^2$$
= $$\frac{22}{7} ×(1.5)^2 = 7.07$$
Again,

Area to be painted silver
= [8 ×(1386-7.07)]
= 8×1378.93
= 11031.44
Area to be painted is 11031.44 $$cm^2$$

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

Area to be painted black
= (8×66) $$cm^2$$
= 528 $$cm^2$$
Cost for painting with black colour
=Rs (528×0.05)
= Rs26.40

Therefore, the total painting cost is:
= Rs(2757.86 +26.40)
= Rs 2784.26