Q : 1    A wooden bookshelf has external dimensions as follows: Height \small =110\hspace{1mm}cm, Depth \small =25\hspace{1mm}cm, Breadth \small =85\hspace{1mm}cm (see Fig. \small 13.31). The thickness of the plank is \small 5\hspace{1mm}cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is \small 20\hspace{1mm} paise per \small cm^2 and the rate of painting is \small 10\hspace{1mm} paise per \small cm^2, find the total expenses required for polishing and painting the surface of the bookshelf.

            

Answers (1)

External dimension od the book shelf = 85\ cm\times25\ cm\times110\ cm

(Note: There is no front face)

The external surface area of the shelf = lh + 2 (lb + bh)
\\ = [85 \times 110 + 2 (85 \times 25 + 25 \times 110)] \\ = (9350 + 9750) \\ = 19100\ cm^2

We know, each stripe on the front surface is also to be polished. which is 5 cm stretch.

Area of front face = [85 \times 110 - 75 \times 100 + 2 (75 \times5)]

\\ = 1850 + 750 \\ = 2600\ cm^2

Area to be polished = (19100 + 2600) = 21700\ cm^2

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

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

Now,

Dimension of inner part = 75\ cm\times15\ cm\times100\ cm

Area to be painted in 3 rows = 3\times[2 (l + h) b + lh]

\\ =3\times [2 (75 + 30) \times 20 + 75 \times 30] \\ = 3\times[(4200 + 2250)] \\ = 3\times6450 \\ = 19350\ cm^2

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

Cost of painting 19350\ cm^2 area = Rs.\ (19350 \times 0.10)= Rs.\ 1935

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

= Rs.\ 6275

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