Answer :

External dimensions of book self,

Length, l = 85cm

Breadth, b = 25 cm

Height, h = 110 cm

External surface area of shelf while leaving out the front face of the shelf

= lh+2(lb+bh)

= [85×110+2(85×25+25×110)] = (9350+9750) = 19100

Therefore External surface area of shelf is 19100 \(cm^2 \)

Area of front face

= [85×110-75×100+2(75×5)]

= 1850+750

= 2600 \( cm^2 \)

\(\therefore \) area is 2600 \( cm^2 \)

Area to be polished

= (19100+2600) \( cm^2 \)

= 21700 \( cm^2 \).

Cost of polishing 1 \( cm^2 \) area = Rs 0.20

Cost of polishing 21700 \( cm^2 \) area Rs. (21700×0.20) = Rs 4340

Dimensions of row of the book shelf

Length(l) = 75 cm

Breadth (b) = 20 cm and

Height(h) = 30 cm

Area to be painted in one row

= 2(l+h)b+lh = [2(75+30)× 20+75×30]

= (4200+2250)

= 6450

So, area is 6450 \( cm^2 \).

Area to be painted in 3 rows

= (3×6450)\( cm^2 \)

= 19350 \( cm^2 \).

Cost of painting 1 \( cm^2 \) area = Rs. 0.10

Cost of painting 19350 \( cm^2 \) area = Rs (19350 x 0.1) = Rs 1935

Total expense required for polishing and painting = Rs. (4340+1935) = Rs. 6275

- 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 \( cm^2 \).
- The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?

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