# 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.

H Harsh Kankaria

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 = $Rs.\ (4340 + 1935)$

$= Rs.\ 6275$

Exams
Articles
Questions