A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see the given 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 painting is 10 paise per cm^{2}, find the total expenses required for polishing and painting the surface of the bookshelf.

#### Solution

External height (*l*) of book self = 85 cm

External breadth (*b*) of book self = 25 cm

External height (*h*) of book self = 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)] cm^{2}

= (9350 + 9750) cm^{2}

= 19100 cm^{2}

Area of front face = [85 × 110 − 75 × 100 + 2 (75 × 5)] cm^{2}

= 1850 + 750 cm^{2}

= 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

It can be observed that length (*l*), breadth (*b*), and height (*h*) of each row of the book shelf is 75 cm, 20 cm, and 30 cm respectively.

Area to be painted in 1 row = 2 (*l *+ *h*) *b* + *lh*

= [2 (75 + 30) × 20 + 75 × 30] cm^{2}

= (4200 + 2250) cm^{2}

= 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 × 0.1)

= Rs 1935

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

= Rs 6275

Therefore, it will cost Rs 6275 for polishing and painting the surface of the bookshelf.