Question

A rectangular water tank measuring $80cm \times 60cm \times 60cm$ is filled from a pipe of cross sectional area $1.5 c{m^2}$, the water emerging at $3.2 m/s$. How long does it take to fill the tank?
A. $12$ minutes
B. $10$ minutes
C. $14$ minutes
D. $15$ minutes

Answer 1

Hint: Here in this question we are given with the volume of the tank, and we know the speed of the water emerging and the cross sectional area from which it is emerging, so we can calculate the rate of volume of water flowed through the pipe by the formula,
Rate of Water flowed $ = $(Cross sectional area) $ \times $ (speed of water).
Now, by this we can calculate the time taken to fill the tank by the formula,
Time taken $ = $ (Volume of the tank) $ \div $ (Rate of Water flowed)

Complete step-by-step answer: In this question first of all we will write the given information then we will start solving it.
So, it is given in the question that
A rectangular water tank measuring $80cm \times 60cm \times 60cm$ is filled, with the help of from a pipe of cross sectional area $1.5c{m^2}$,
The water is emerging at a speed of $3.2m/s$.
So, first of all we will find the volume of the tank which is to be filled, for which we know that
Water tank measures $80cm \times 60cm \times 60cm$
From this we can say that,
Length of the tank $ = 80cm$, Breadth of the tank $ = 60cm$, Height of the tank $ = 60cm$,
As the Volume of the tank $ = L \times B \times H$
So, now by putting the corresponding values we get
Volume of the tank $ = 80 \times 60 \times 60c{m^3}$
Volume of the tank $ = 288000c{m^3}$
Now, as we know that
The water is emerging at a speed of $3.2m/s$.
Which can also be said that, The speed of the emerging water is $3.2m/s = 320cm/s$. (As $1m = 100cm$)
The pipe has a cross sectional area of $1.5c{m^2}$
So, from these we can calculate the rate of volume of water flowed through the pipe by the formula,
Rate of Water flowed $ = $(Cross sectional area) $ \times $ (speed of water).
So, here as we mentioned that, Cross sectional area $ = 1.5c{m^2}$, speed of water $ = 320cm/s$
Rate of Water flowed $ = $ $1.5 \times 320c{m^3}/s$
Now the time taken to fill the water tank will be equal to the volume of the tank divided by The Rate of Water flowed.
So, Time taken to fill the tank$ = $(Volume of the tank) $ \div $ (Rate of Water flowed)
Now here, as we know that Volume of the tank $ = 288000c{m^3}$,
 Rate of Water flowed $ = $ $1.5 \times 320c{m^3}/s$
So, Time taken to fill the tank$ = \dfrac{{288000}}{{480}}$
Time taken to fill the tank$ = 600\sec $
$ \Rightarrow $ Time taken to fill the tank$ = 10$ minutes (As $1$minute$ = 60$seconds)

So, the correct answer is “Option B”.

Note: Here in this question the concept which is used is that the rate of the volume filled by the water will be equal to the multiplication of the cross sectional area of the pipe from which water is emerging into the speed by which water is emerging.