Question

A rectangular tank of length \[37\dfrac{1}{3}\] m internally, 12 m in breadth and 8 m in depth is full of water. Find the weight of water in metric tons, given that one cubic metre of water weighs 1000 kg.

Answer 1

Hint: We have to find the shape of a rectangular tank. For the determined shape, we should apply the formula to find the volume of the figure. We know that the volume of 3D figure is equal to product of base of 3D figure and depth of 3D figure. The base of the 3D figure is a rectangle. The area of the base of the 3D figure is equal to the product of length of base and breadth of base. All the given measurements of the rectangular tank are in m. So, we will find the volume in \[{{\text{m}}^{3}}\], we should convert it into units of metric tons. In the question, it is given that a metric ton is equal to 1000 kg.

Complete step-by-step solution -
From the question, it is given that a rectangular tank of length \[37\dfrac{1}{3}m\] internally, 12 m in breadth and 8 m in depth is full of water. It is clear that the length, breadth and height of the tank are different. If a figure has different length, breadth and height, then it is said to be a cuboid.
We know that the volume of cuboid is equal to \[lbh\]where l represents length of cuboid, b represents breadth of cuboid and h represents height of cuboid.

It is given that the length of the tank is equal to \[37\dfrac{1}{3}m\], the breadth of the tank is equal to 12 m and height of the tank is equal 8 m.
\[\begin{align}
  & \text{Volume of tank = }\left( 37\dfrac{1}{3} \right)\left( 12 \right)(8){{m}^{3}} \\
 & \Rightarrow \text{Volume of tank = }\left( \dfrac{111}{3} \right)\left( 12 \right)(8){{m}^{3}} \\
 & \Rightarrow \text{Volume of tank = 3552 }{{\text{m}}^{3}} \\
 & \\
\end{align}\]
It is given that a cubic metre of water weighs 1000kg.
Let us assume \[\text{3552 }{{\text{m}}^{3}}\] of water weighs x kg.
\[\begin{align}
  & 1\to 1000 \\
 & 3552\to x \\
\end{align}\]
By criss-cross method,
\[\begin{align}
  & 1.x=1000\times 3552 \\
 & \Rightarrow x=3552000{{m}^{3}} \\
\end{align}\]
So, the weight of water is \[3552000kg\] if the volume is \[\text{3552 }{{\text{m}}^{3}}\].
We know that 1000kg is equal to 1 metric ton.
So, the volume of water in a rectangular tank is equal to \[3552\text{ metric ton}\].

Note: We should be careful while converting one unit from other units. In this sum, if we write \[c{{m}^{3}}\] instead of \[{{m}^{3}}\]. The final answer will be totally incorrect. At the end of the solution, the student should know that \[1000\text{ }{{m}^{3}}\]is equal to 1 metric ton. We should be careful to convert a mixed fraction into an improper fraction. The area of the base of the rectangular tank is equal to the internal length of tank and breadth of tank.