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.

Answer 1

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

Surface area of wooden sphere = 4πr²

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

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

Height (h) of cylindrical support = 7 cm

CSA of cylindrical support = 2πrh

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

Area of the circular end of cylindrical support = πr² 

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

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

= (8 × 1378.93) cm² = 11031.44 cm²

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

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

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.