An open box is made of wood $3\ cm$ thick. Its external length, breadth and height are $1.48\ m, 1.16\ m$ and $8.3\ dm$. Find the cost of painting the inner surface of $Rs.\ 50$ per sq. metre.

Given:

An open box is made of wood $3\ cm$ thick. Its external length, breadth and height are $1.48\ m, 1.16\ m$ and $8.3\ dm$.

To do:

We have to find the cost of painting the inner surface of $Rs.\ 50$ per sq. metre.

Solution:

Length of open wood box $(L) = 1.48\ m$

$= 148\ cm$

Breadth $(B) = 1.16\ m$

$= 116\ cm$

Height $(H) = 8.3\ dm$

$= 83\ cm$

Thickness of wood $= 3\ cm$

This implies,

Inner length $(l)=148-2 \times 3$

$=148-6$

$=142 \mathrm{~cm}$

Height $(h)=83-3$

$=80 \mathrm{~cm}$

Breadth $(b)=116-2 \times 3$

$=116-6$

$=110 \mathrm{~cm}$

Therefore,

Surface area of inner box $=2 h(l+b)+lb$

$=2 \times 80(142+110)+142 \times 110$

$=160(252)+15620$

$=40320+15620$

$=55940 \mathrm{~cm}^{2}$

$=\frac{55940}{10000}$

$=5.594 \mathrm{~m}^{2}$

Rate of painting $=Rs.\ 50$ per $\mathrm{m}^{2}$

Total cost of painting $= Rs.\ 50 \times 5.594$

$=Rs.\ 279.70$

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Updated on: 10-Oct-2022

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