Answer

Verified

452.4k+ views

Hint-Using the formula of volume of pipe ,first find out the height of the pipe and then solve it further.

Complete step-by-step answer:

Given that tank is in the form of a cuboid where

Length=l=50m

Breadth=b=44m

Height=h=21cm=$\frac{{21}}{{100}}$ m (because the level of the water in the tank should raise by 21cm)

So, the volume of the tank=

$\begin{gathered}

l \times b \times h \\

= 50 \times 44 \times \frac{{21}}{{100}} \\

= \frac{{44 \times 21}}{2} \\

= 462c{m^3} \\

\\

\end{gathered} $

Now , also let us try to find out the volume of the pipe,

The pipe is in the form of a cylinder

So, the volume of the cylinder is given by the equation

$V = \pi {r^2}h$

So, now lets substitute these values here

We are given with the diameter of the pipe, so let us find out the radius of the cylinder

Radius=$\frac{{diameter}}{2} = \frac{{14}}{2} = 7cm$

So, from this we get the volume of the pipe to be equal to

Volume=$\frac{{22}}{7} \times {\left( {\frac{7}{{100}}} \right)^2}h$

Volume$ = \frac{{22 \times 7}}{{10000}}h$

Now, since the water is flowing through the pipe and then reaching the tank, we can write that

The Volume of pipe=Volume of tank

So, we get$\frac{{22 \times 7}}{{10000}}h = 462c{m^3}$

So, we get h=$\frac{{22 \times 21 \times 10000}}{{22 \times 7}}$

h=30,000m

Now since the rate is expressed in km/hr we will convert this height h to km

So, we get height h=30km

S0,

We have 15km travels in pipe in 1 hour

1km travels in pipe in =$\frac{1}{{15}}hour$

The total height travelled was 30km

So, the time taken to travel 30 kilometres=$\frac{{30}}{{15}} = 2$ hours

So, the total time taken is 2 hours for the tank to be filled

Note: Whenever we have been given with the diameter of a quantity make sure to obtain the value of the radius from this and then apply it in the formula, do not apply the value of diameter in the formula

Complete step-by-step answer:

Given that tank is in the form of a cuboid where

Length=l=50m

Breadth=b=44m

Height=h=21cm=$\frac{{21}}{{100}}$ m (because the level of the water in the tank should raise by 21cm)

So, the volume of the tank=

$\begin{gathered}

l \times b \times h \\

= 50 \times 44 \times \frac{{21}}{{100}} \\

= \frac{{44 \times 21}}{2} \\

= 462c{m^3} \\

\\

\end{gathered} $

Now , also let us try to find out the volume of the pipe,

The pipe is in the form of a cylinder

So, the volume of the cylinder is given by the equation

$V = \pi {r^2}h$

So, now lets substitute these values here

We are given with the diameter of the pipe, so let us find out the radius of the cylinder

Radius=$\frac{{diameter}}{2} = \frac{{14}}{2} = 7cm$

So, from this we get the volume of the pipe to be equal to

Volume=$\frac{{22}}{7} \times {\left( {\frac{7}{{100}}} \right)^2}h$

Volume$ = \frac{{22 \times 7}}{{10000}}h$

Now, since the water is flowing through the pipe and then reaching the tank, we can write that

The Volume of pipe=Volume of tank

So, we get$\frac{{22 \times 7}}{{10000}}h = 462c{m^3}$

So, we get h=$\frac{{22 \times 21 \times 10000}}{{22 \times 7}}$

h=30,000m

Now since the rate is expressed in km/hr we will convert this height h to km

So, we get height h=30km

S0,

We have 15km travels in pipe in 1 hour

1km travels in pipe in =$\frac{1}{{15}}hour$

The total height travelled was 30km

So, the time taken to travel 30 kilometres=$\frac{{30}}{{15}} = 2$ hours

So, the total time taken is 2 hours for the tank to be filled

Note: Whenever we have been given with the diameter of a quantity make sure to obtain the value of the radius from this and then apply it in the formula, do not apply the value of diameter in the formula

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Establish a relation between electric current and drift class 12 physics CBSE

Guru Purnima speech in English in 100 words class 7 english CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Copper is not used as potentiometer wire because class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE