Height = 110cm, Depth = 25cm, Breadth = 85cm (see figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing-is 20 paise per $$cm^2$$and the rate of pointing is 10 paise per $$cm^2$$ find the total expenses required for palishing and painting the surface of the bookshelf.

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