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 metre sheet , sheet being $2$ m wide.

Answer 1

Hint: We are given the iron tank and its dimensions i.e. length, breadth and height are given. We are asked to find the total cost of the sheet if the cost of per meter sheet is given. For this we will first find the total surface area of the iron tank using length, breadth and height. After finding the area we will divide the area by the width given of the sheet. To find the cost of the sheet used. We will multiply the total length obtained by the cost per meter of the sheet.

Formula used: Area of the tank= 2(lb+bh+lh)
Here l=length, b=breadth, h= height
Length of iron sheet=$dfrac{\text{Area of tank}}{\text{width}}$
Total cost = cost per meter× length of sheet

Complete step-by-step answer:
Step1: The given l$ = 12$m, b$ = 9$m and h$ = 4$m of the iron tank. We will find the area of the tank
Area=2(lb+bh+lh)
On substituting the values in the formula we get:
Area$ = 2(12 \times 9 + 9 \times 4 + 4 \times 12)$
On solving the expression we get:
Area$ = (108 + 36 + 48)$
On adding the expressions we get:
Area$ = 2(192)$
On multiplying we get:
Area $ = 384$$cm^2$
Step2: We will find the length of the sheet on dividing the area by the width
Length of iron sheet=Area of tankwidth
On substituting the values here width$ = 2$m
length$ = \dfrac{{384}}{2}$
on dividing we get:
length $ = 192$cm
Step3: To find the total cost of the iron sheet used. We will multiply the cost/m by the total length. Here cost per meter is Rs $5$
Hence total cost is:
$192 \times 5 = 360$

Final answer: Total cost is Rs$360$

Note: In such types of questions get confused in the application of formula and they also get confused how to find the length of the sheet. They must keep in mind they have to find total surface area.
Area of the tank= 2(lb+bh+lh)