# A petrol tank is in the shape of a cylinder with hemisphere of same radius attached to both ends. If the total length of the tank is $6m$ and the radius is $1m$, what is the capacity of the tank in litres.

Answer

Verified

203.4k+ views

**Hint:**The petrol tank is in the shape of a cylinder with two hemispheres of same radii attached to the both sides. The capacity of the tank is equal to the total volume of the tank. Volume of the tank is equal to the sum of the volumes of the cylinder and two hemispheres.

**Complete step-by-step answer:**

Let us note down the given data.

A petrol tank is in the shape of a cylinder with hemisphere of same radius attached to both ends.

The total length of the tank is $6m$

The radius is $1m$.

Here the radius refers to the radius of the hemisphere and the cylinder also.

So, let us draw the diagram as per the above data,

As the total length of the tank is $6m$ and the radius of the hemisphere is $1m$,

The length of the cylinder is $6 - 2\left( 1 \right) = 4m$

Now the volume of the tank is equal to the sum of the volumes of cylinder and two hemispheres.

Volume of the cylinder $ = \pi {r^2}h$

As we know the value of $r$ is $1$ and $h$ is $4$.

Substitute in the above formula,

Volume of cylinder $ = \pi \times {1^2} \times 4$

$ = 4\pi $

Now, volume of hemisphere $ = \dfrac{2}{3}\pi {r^3}$

Substituting the values, we get,

Volume of hemisphere $ = \dfrac{2}{3}\pi {\left( 1 \right)^3}$

$ = \dfrac{{2\pi }}{3}$

Now, the capacity of the tank $ = $ Volume of the tank

$ = $ Volume of cylinder $ + $ $2 \times $ Volume of hemisphere

\[

= 4\pi + 2 \times \dfrac{{2\pi }}{3} \\

= \dfrac{{12\pi + 4\pi }}{3} \\

= \dfrac{{16\pi }}{3} \\

\]

We know the value of $\pi $ as $\dfrac{{22}}{7}$, if we substitute that in the above, we get,

Volume of the tank $ = \dfrac{{16}}{3} \times \dfrac{{22}}{7}$

$

= \dfrac{{352}}{{21}} \\

= 16.761{m^3} \\

$

And we are asked to find out the capacity of the tank in litres. So, we know that $1{m^3} = 1000litres$. Apply in the above answer, we get

Volume of the tank or Capacity of the tank $ = 16.761 \times 1000$

$ = 16761litres$.

Hence the capacity of tank in litres is $16761litres$

**Note:**This type of mensuration problem can be solved easily when we get a clear idea about the shapes of the solids that are involved in the body. We are able to solve this problem in other ways also. Anyways we are calculating the volume of hemisphere and multiplying it with two to get the volume of two hemispheres. But we can directly find the volume of the sphere as those two hemispheres are identical. It will also give the same answer.

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

The coordinates of the points A and B are a0 and a0 class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

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

List out three methods of soil conservation

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

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE