Question

A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm.

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 cm² and the rate of painting is 10 paise per cm² , find the total expenses required for polishing and painting the surface of the bookshelf.

Answer 1

Outer length, l = 25 cm. 

outer breadth, b = 85 cm. 

outer height, h = 110 cm. 

Outer surface area = lh + 2lb + 2bh = lh + 2(lb + bh) 

= 85 × 110 + 2(85 × 25 + 25 × 110) 

= 9350 + 9750 = 19100 cm² . 

Area of front face, 

= [85 × 110 – 75 × 100 + 2(75 × 5)] 

= (9350 – 7500 + 2(375)] 

= 9350 – 7500 + 750 

= 11000 – 7500 = 3500 cm² . 

Area to be polished, 

= 19100 + 3500 = 22600 cm² . 

Cost of polishing 1 cm³ is Rs. 0.20. 

Cost of polishing 22600 cm³ … ? … 

= 22600 × 0.20 = Rs. 4520. 

Length of horizontal shelf, l = 75 cm. 

breadth, b = 20 cm. 

height, h = 30 cm. 

Area of horizontal shelf = 2(l + h)b + lh 

= [2(75 + 30) × 20 + 75 × 30]

 = (4200 + 2250] cm² . = 6450 cm² . 

∴ Area of painting 3 horizontal rows 

= 3 × 6450 

= 19350 cm² . 

Cost of painting for 1 cm³ is Rs. 0.10. 

∴ Cost of painting 19350 cm³ … ? 

= 19350 × 0.10 = Rs. 1935. 

∴ Total cost of polish and painting 

= Rs. 4520 + Rs. 1935 

= Rs. 6455.