#### 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 cm^{2} and black paint costs 5 paise per cm^{2}.

#### Solution

Radius (*r*) of wooden sphere = (21/2)cm = 10.5cm

Surface area of wooden sphere = 4π*r*^{2}

`=[4xx22/7xx(10.5)^2]cm^2 = 1386cm^2`

Radius (*r*_{1}) of the circular end of cylindrical support = 1.5 cm

Height (*h*) of cylindrical support = 7 cm

CSA of cylindrical support = 2π*rh*

`=[2xx22/7xx(1.5)xx7]cm^2 = 66cm^2`

Area of the circular end of cylindrical support = π*r*^{2}

`=[22/7xx(1.5)^2]cm^2=7.07cm^2`

Area to be painted silver = [8 × (1386 − 7.07)] cm^{2}

= (8 × 1378.93) cm^{2} = 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) = 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.