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 $c{m^2}$ and rate of painting is 10 paise per $c{m^2}$. Find the total expense required for polishing and painting the surface of the bookshelf.

Answer 1

Hint: Here we need to find both external surface area and internal surface area to calculate the total expense for polishing and painting the surface of the bookshelf.

Complete step-by-step answer:
We have been given that
External length (l) of bookshelf =85cm
External breadth (b) of bookshelf =25cm
External height (h) of bookshelf =110cm
External surface area of bookshelf while leaving out the front face of the shelf=$lh + 2(lb + bh)$
$
   = (85 \times 110) + 2(85 \times 25 + 25 \times 110) \\
   = 9350 + 9750 \\
   = 19100{\text{ c}}{{\text{m}}^2} \\
$
Area if front face=$(85 \times 100) - 75 \times 100 + 2(75 \times 5) = 1850 + 760 = 2600{\text{ c}}{{\text{m}}^2}$
Area to be polished$ = 19100 + 2600 = 21700{\text{ c}}{{\text{m}}^2}$
Cost of polishing= $Rs.21700 \times 0.20 = Rs.4340$
Length, breadth, height of each row of bookshelf are 75 cm, 20 cm, and 30 cm respectively.
From the figure area to be painted in 1 row=$2(l + b) + lh$
$
   = 2(75 + 30)20 + 75 \times 30 \\
   = 6450{\text{ c}}{{\text{m}}^2} \\
$
Area to be painted in 3 rows$ = 3 \times 6450 = 19350{\text{ c}}{{\text{m}}^2}$
Total cost of painting$ = Rs.(19350 \times 0.1) = Rs.1935$
Total expenses $ = Rs.(4340 + 1935) = Rs.6275$

Note: In this question it must be remembered to find the length of the open portion separately and for the painting area to be painted in 3 rows must be found.