Question

A rectangular tank, 8m long, 7m wide and 5m high, contains water to a depth of 3m. How much more water can it hold?

Answer 1

Hint:
We will first consider the dimensions of the rectangular tank given and the water depth. As we need to find how much water can it hold in the tank, we will first find the volume of the tank using the given dimensions and formula of volume of a cuboid. Then we will find the volume of water in the tank using the same formula of the cuboid. Now, to find how much the tank can hold, we will subtract the volumes and get the extra volume of water it can hold.

Complete step by step solution:
We will first consider the given dimensions of the water tank and the dimensions of the water in the tank.
The objective is to find how much water the tank can hold.
We will first find the volume of the tank using the formula of the cuboid that is \[V = lbh\].
As dimensions are given as 8m long, 7m wide and 5m high, we will substitute the values in the formula,
Thus, we get,
\[
   \Rightarrow V = 8 \times 7 \times 5 \\
   \Rightarrow V = 280{m^3} \\
 \]
Next, we will find the volume of water in the tank by using the dimensions as 8m long, 7m wide and 3m high.
The formula we will use is \[V = lbh\].
Thus, we get,
\[
   \Rightarrow V = 8 \times 7 \times 3 \\
   \Rightarrow V = 168{m^3} \\
 \]
Now, as we need to determine the extra volume of water it can hold, we will subtract the obtained volumes from each other.
Thus, we get,
\[
   \Rightarrow V = 280 - 168 \\
   \Rightarrow V = 112{m^3} \\
 \]

Hence, we can conclude that the tank can hold \[112{m^3}\] more water in its tank.

Note:
As we have to find the extra water filled in the tank, so, we just have subtracted the volume of water filled in the tank from the volume of the tank. No need for converting the units as all the dimensions given are in the same units. It is necessary to calculate the values of both the volumes and then subtract the higher from the lower.