A closed iron tank $12\ m$ long, $9\ m$ wide and $4\ m$ deep is to be made. Determine the cost of iron sheet used at the rate of $Rs.\ 5$ per metre sheet, sheet being $2\ m$ wide.
Given:
A closed iron tank $12\ m$ long, $9\ m$ wide and $4\ m$ deep is to be made.
To do:
We have to find the cost of iron sheet used at the rate of $Rs.\ 5$ per metre sheet, sheet being $2\ m$ wide.
Solution:
Length of the iron tank $(l) = 12\ m$
Breadth of the tank $(b) = 9\ m$
Depth of the tank $(h) = 4\ m$
Total surface area of the sheet used $=2(lb+b h+lh)$
$=2(12 \times 9+9 \times 4+4 \times 12)$
$=2(108+36+48)$
$=2 \times 192$
$=384 \mathrm{~m}^{2}$
Width of the sheet $=2 \mathrm{~m}$
Therefore,
Length $=\frac{\text { Area }}{\text { Width }}$
$=\frac{384}{2}$
$=192 \mathrm{~m}$
Rate of $1 \mathrm{~m}$ of sheet $= Rs.\ 5$
This implies,
Total cost $=Rs.\ 192 \times 5$
$=Rs.\ 960$
The cost of iron sheet used is Rs. 960.
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