Length of bookshelf (l) = 85cm
Breadth of bookshelf (b) = 25 cm
Height of bookshelf (h) = 110cm
We have to find out the total expenses required for polishing and painting the surface of the bookshelf.
To calculate the external surface area of the shelf while leaving out the front face of the shelf = lh+2(lb+bh)
= 19100 cm2
Hence, the external surface area of shelf is 19100 cm2
Area of front face = [85×110-75×100+2(75×5)]
= 2600 cm2
Thus, the area is 2600 cm2
Area to be polished surface = (19100+2600) cm2
= 21700 cm2
Given cost of polishing 1 cm2 area = Rs 0.20
Therefore, the cost of polishing 21700 cm2 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]
So, area is 6450 cm2.
Area to be painted in 3 rows = (3×6450)cm2 = 19350 cm2.
Cost of painting 1 cm2 area = Rs. 0.10
Cost of painting 19350 cm2 area = Rs (19350 x 0.1) = Rs 1935
Total expense required for polishing and painting = Rs. (4340+1935) = Rs. 6275
The cost for polishing and painting the surface of the bookshelf is Rs. 6275.