Answer

Verified

450.6k+ views

Hint: Start with finding the total volume of liquid by finding the volume of the bowl. Then compare it with the total volume of cylindrical bottles ensuring that 10% of liquid is lost while transferring it.

According to the question, the diameter of the bowl is 36 cm. Then its radius is 18 cm.

$ \Rightarrow r = 18cm$

We know that the volume of a hemispherical bowl is $\dfrac{2}{3}\pi {r^3}$. Using this formula, we’ll get:

$

\Rightarrow V = \dfrac{2}{3} \times \dfrac{{22}}{7} \times {\left( {18} \right)^3}, \\

\Rightarrow V = \dfrac{{44 \times 5832}}{{21}}, \\

\Rightarrow V = 12219.43c{m^3} \\

$

Thus, the total volume of liquid is $12219.43c{m^3}$.

Given, the diameter of the cylinder is 6 cm. Thus, its radius is 3 cm.

We know that the volume of the cylinder is $\pi {r^2}h$. And we have 72 cylindrical bottles. So, total volume is:

$

\Rightarrow V = 72 \times \pi \times {\left( 3 \right)^2}h, \\

\Rightarrow V = 72 \times \dfrac{{22}}{7} \times 9h \\

$

Now, from the total volume of liquid calculated above (i.e. $12219.43c{m^3}$), 10% is lost while transferring it. The volume of liquid left is 90% of $12219.43c{m^3}$. And this volume must be equal to the total cylindrical bottle’s volume. So, we have:

$

\Rightarrow 72 \times \dfrac{{22}}{7} \times 9h = 90\% {\text{ of }}12219.43c{m^3}, \\

\Rightarrow 72 \times \dfrac{{22}}{7} \times 9h = \dfrac{{90}}{{100}} \times 12219.43, \\

\Rightarrow h = \dfrac{{7 \times 12219.43}}{{72 \times 22 \times 10}}, \\

\Rightarrow h = \dfrac{{85536.01}}{{15840}}, \\

\Rightarrow h = 5.4cm \\

$

Thus the height of each cylindrical bottle is 5.4 cm. (C) is the correct option.

Note: Volume of liquid is conserved in the above question.

$ \Rightarrow $Volume of liquid stored in the bowl $ = $volume of liquid transferred in bottles $ + $volume of liquid lost while transferring it.

This is the key principle for solving such types of problems.

According to the question, the diameter of the bowl is 36 cm. Then its radius is 18 cm.

$ \Rightarrow r = 18cm$

We know that the volume of a hemispherical bowl is $\dfrac{2}{3}\pi {r^3}$. Using this formula, we’ll get:

$

\Rightarrow V = \dfrac{2}{3} \times \dfrac{{22}}{7} \times {\left( {18} \right)^3}, \\

\Rightarrow V = \dfrac{{44 \times 5832}}{{21}}, \\

\Rightarrow V = 12219.43c{m^3} \\

$

Thus, the total volume of liquid is $12219.43c{m^3}$.

Given, the diameter of the cylinder is 6 cm. Thus, its radius is 3 cm.

We know that the volume of the cylinder is $\pi {r^2}h$. And we have 72 cylindrical bottles. So, total volume is:

$

\Rightarrow V = 72 \times \pi \times {\left( 3 \right)^2}h, \\

\Rightarrow V = 72 \times \dfrac{{22}}{7} \times 9h \\

$

Now, from the total volume of liquid calculated above (i.e. $12219.43c{m^3}$), 10% is lost while transferring it. The volume of liquid left is 90% of $12219.43c{m^3}$. And this volume must be equal to the total cylindrical bottle’s volume. So, we have:

$

\Rightarrow 72 \times \dfrac{{22}}{7} \times 9h = 90\% {\text{ of }}12219.43c{m^3}, \\

\Rightarrow 72 \times \dfrac{{22}}{7} \times 9h = \dfrac{{90}}{{100}} \times 12219.43, \\

\Rightarrow h = \dfrac{{7 \times 12219.43}}{{72 \times 22 \times 10}}, \\

\Rightarrow h = \dfrac{{85536.01}}{{15840}}, \\

\Rightarrow h = 5.4cm \\

$

Thus the height of each cylindrical bottle is 5.4 cm. (C) is the correct option.

Note: Volume of liquid is conserved in the above question.

$ \Rightarrow $Volume of liquid stored in the bowl $ = $volume of liquid transferred in bottles $ + $volume of liquid lost while transferring it.

This is the key principle for solving such types of problems.

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

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Difference Between Plant Cell and Animal Cell

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

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How many crores make 10 million class 7 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE