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