Question

The water tank with length 4m breadth 1.5m and height 1m is completely filled with water, if it is to be emptied using a bucket of capacity 8 litres, find how many times the bucket should be used to empty the tank completely. \[\]
A.75\[\]
B.750\[\]
C.300\[\]
D.600\[\]

Answer 1

Hint: We recall the definition of cuboid and its formula for volume $V=l\times b\times h$. We find how much water will be contained by volume of $1{{\text{m}}^{3}}$. We find the volume of the cube , the amount of water it contains ${{V}_{l}}$ and then the number of times bucket should be used to empty the tank completely as $\dfrac{{{V}_{l}}}{8}$. \[\]

Complete step by step answer:
We know that a cuboid is a three dimensional object with six rectangular faces joined by 8 vertices. It has three different types of sides called length, breadth parallel to ground and height vertical to ground denoted respectively as $l,$$b$ and $h$. \[\]
The amount of space contained by a three dimensional object is measured by the quantity called volume. The amount of space that is occupied by a cuboid is the product of length, breadth and height. Mathematically, volume $V$ of a cuboid is.
\[V=l\times b\times h\]
If length, breadth and height are equal then we call the cuboid a cube. The amount of water contained in the space by a cube of 1cm is called 1 millilitre(ml). So the 1ml water is contained in $1cm\times 1cm\times 1cm=1c{{m}^{3}}$ of space. So now we find how much water is contained in a cube with a side 1metre (m).
 The amount of space contained by a cube of 1m is
\[V=1m\times 1m\times 1m=100cm\times 100cm\times 100cm=100000c{{m}^{3}}\]
We know that 1000ml=1litre. $1c{{m}^{3}}$ of space contains $1\text{ml}=\dfrac{1}{1000}\text{litre}$ of water. So $1000000c{{m}^{3}}$ of space will be contained \[\text{1}000000\text{ml}=\text{1}000000\times \dfrac{1}{1000}\text{=1}000\text{ litre}\] of water.
We find that a cube with side 1m or $1{{m}^{3}}$of space will contain 1000litre of water. We are given the question that the water tank has length $l=4$m, breadth $b=1.5$m , height $h=1$m. It is in cuboid shape.
 

 The volume of the cuboid shaped water tank is
\[V=lbh=4\text{m}\times 1.5\text{m}\times 1\text{m}=6{{\text{m}}^{3}}\]
The total amount of water above water tank contains is
\[{{V}_{l}}=6\times 1000\text{litre}=6000\text{litre}\]
The amount of water that is extracted in one time by the bucket is ${{V}_{b}}=8$ litre. The number of times required to empty the water tank is
\[\dfrac{{{V}_{l}}}{{{V}_{b}}}=\dfrac{6000}{8}=750\]

So, the correct answer is “Option B”.

Note: The other liquid with different densities may not have 1ml of liquid in a cube of side 1cm. The liquid with unit density can fill 1ml in a cube of 1cm , for example water. Water tanks are built in cylindrical or cuboid shape. The cylindrical shape requires radius of the base $r$ and height $h$ if we want to find the volume$\pi {{r}^{2}}h$.