A wooden bookshelf has external dimensions as follows: Height = 1… - Vidyadip

Question

A wooden bookshelf has external dimensions as follows: Height $= 110\ cm$, Depth $= 25\ cm,$ Breadth $= 85\ cm$ (See 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 $cm^2$. Find the total expenses required for polishing and painting the surface of the bookshelf.

✓

Answer

External length of book shelf $=85 cm$
Breadth $=25 cm$
Height $=110 cm$
External surface area of shelf while leaving front face of shelf
$lh +2( lb + bh )[85 \times 110+2(85 \times 25+25 \times 110)]$ $19100 cm^2$
Area of Front face $=[85 \times 110-75 \times 100+2(75 \times 5)] cm ^2=1850+750 cm^2=2600 cm^2$
Area to be polished $=19100+2600 cm^2=21700 cm^2$
Cost of polishing $1 cm^2$ area $=₹ 0.20=₹ 4340$
Now, Length $(I)$, breadth $(b)$, height $(h)$ of each row of book shelf is $75\ cm, 20\ cm$ and $30\ cm$ $=\left(\frac{110-20}{3}\right)$ respectively.
Area to be painted in $1 row =2(1+ h ) b + lh [2(75+30) \times 20+75 \times 30)] cm ^2(4200+2250) cm ^2 6450 cm^2$
Area to be painted in $3$ rows $=3 \times 6450=₹ 1935\ cm^2$

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