Question

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 Rs. 5 per meter sheet, sheet being 2 m wide.

Answer 1

Hint – In this question first find out, total surface area of the closed iron tank which is given as $S.A = 2\left( {lb + bh + hl} \right)$ where symbols have their usual meaning, later on divide this area to the width of the sheet to get the required length of the sheet, so use this concept to reach the solution of the question.

Given data
Length (l) of iron tank = 12m
Breath (b) of iron tank = 9m
Height (h) of iron tank = 4m
So, it is given that the iron tank is closed (see figure) therefore it has total six walls (see figure), and so the total surface area (S.A) of these walls is given as
$S.A = 2\left( {lb + bh + hl} \right)$
So, substitute the given values in above equation we have,
$
   \Rightarrow S.A = 2\left( {12 \times 9 + 9 \times 4 + 4 \times 12} \right) \\
   \Rightarrow S.A = 2\left( {108 + 36 + 48} \right) = 2\left( {192} \right) = 384{m^2} \\
$
Now it is given that the sheet is 2 m wide.
So, length of the sheet required to make a closed iron tank $ = \dfrac{{384{\text{ }}{{\text{m}}^2}}}{{2{\text{ m}}}} = 192{\text{ m}}$
Now it is also given that the cost of iron sheet is Rs. 5 per meter sheet.
So, the total cost of iron sheet to make a closed iron tank $ = 192 \times 5 = 960{\text{ Rs}}{\text{.}}$
So, this is the required answer.

Note – in such types of questions the key concept we have to remember is that always recall the formula of total surface area which is stated above, then use this formula to calculate the surface area of the iron tank, then calculate the length of sheet required to make a closed iron tank by dividing the width of sheet to the surface area of the iron tank, then multiply this value to the cost of per sheet which is given, we will get the required cost of iron sheet to make a closed iron tank.