Question

A water tank is 30 m long, 20 m wide and 12 m deep. It is made up of iron sheet which is 3 m wide. If the cost of the iron Sheet is Rs 10 per meter, then the total cost of the iron sheet required to build the tank is
A) Rs. 6000
B) Rs. 8000
C) Rs. 9000
D) Rs. 10000

Answer 1

Hint:
Here we will firstly find the value of the total surface area of the tank. Then we will find the length of the required sheet by equating it to the total surface area of the tank. Then we will simply multiply the length of the required length of the sheet with the price given to get the total cost of the iron sheet required to build the tank.

Complete Step by Step Solution:
The dimensions of the water tank are 30 m long, 20 m wide and 12 m deep.
Firstly we will find the total surface area of the tank which is of the shape of a rectangle. Therefore, we get
Surface area of the tank \[ = 2\left( {L \times B + B \times H + L \times H} \right)\]
Where, \[L\] is the length of the tank, \[B\] is the breadth of the tank, \[H\] is the height of the tank. Therefore, by putting the values of the length, breadth and height of the tank in the formula, we get
Surface area of the tank \[ = 2\left( {30 \times 20 + 20 \times 12 + 30 \times 12} \right)\]
Now by solving this, we get
Surface area of the tank \[ = 2\left( {600 + 240 + 360} \right)\]
Surface area of the tank \[ = 2\left( {1200} \right) = 2400{m^2}\]
So, the area of the sheet required is \[2400{m^2}\].
It is given that it is made up of iron sheet which is 3 m wide. We have to find the length of the sheet. Therefore, we get
Area of the sheet required \[ = l \times w = 2400{m^2}\].
Now by putting the value of the width of the sheet and solving it, we will get the value of the length of the sheet. Therefore, we get
\[ \Rightarrow l \times 3 = 2400\]
\[ \Rightarrow l = \dfrac{{2400}}{3} = 800m\]
So the length of the required sheet is equal to \[800m\].
It is given that the cost of the iron Sheet is Rs 10 per meter. Therefore, by multiplying the length of the sheet with the price given, we will get the total cost of the iron sheet required to build the tank. Therefore, we get
Total cost \[ = 800 \times 10 = Rs.8000\]
Hence the total cost of the iron sheet required to build the tank is Rs. 8000.

So, option B is the correct answer.

Note:
Surface area of an object or shape is the sum of all the areas of the faces of an object or shape and surface area is generally measured in square units. Area is the amount of surface covered by a shape in two dimensional. Perimeter is the total length of the outer boundary of a shape in two dimensional which is the sum of all the edges of the figure. Perimeter is measured in meters. Volume is the amount of space occupied by an object in three-dimensional space. Volume is measured in cubic meters.
It is compulsory to write the units after the calculated values while solving a problem, it plays an important role.