Question

Find the capacity (in liters) of a cylindrical storage tank of height 1.2 m and base diameter 35 cm.

Answer 1

- Hint: First of all consider the cylinder of height 1.2m and diameter 35 cm. Now, find the radius by using \[\dfrac{diameter}{2}\]. Now, use the formula for finding the volume of the cylinder that is \[\pi {{r}^{2}}h\] and use it to get the required answer.

Complete step-by-step solution -

In this question, we have to find the capacity of a cylindrical storage tank of height 1.2 m and base diameter 35 cm in liters. Before proceeding with the question, let us know what the capacity of a vessel means. Basically, the capacity is nothing but the volume of the vessel or the amount of the liquid or any other substance, a vessel or a container can hold. Whenever we are asked to find the capacity of a container or vessel, we need to find its volume. We generally express capacity in terms of liters, milliliters, etc.
Now, let us consider our question. Here, we are given a cylinder of 1.2m height and a diameter of 35 cm. Let us draw the cylinder to visualize the question.

We know that the volume of the cylinder is \[\pi {{r}^{2}}h\] where r is the radius of the cylinder and h is the height of the cylinder. We are given that the height of the cylinder = 1.2m \[=1.2\times 100=120cm\]
We are given that the diameter of the cylinder d = 35 cm.
We know that,
\[Radius=\dfrac{Diameter}{2}\]
So, we get, the radius of the cylinder,
\[r=\dfrac{diameter}{2}=\dfrac{35}{2}cm\]
Let us substitute the value of h = 120 cm and \[r=\dfrac{35}{2}cm\] in the volume of the cylinder. So, we get,
The volume of the cylinder \[=\pi {{r}^{2}}h\]
\[=\pi {{\left( \dfrac{35}{2} \right)}^{2}}\left( 120 \right)c{{m}^{3}}\]
By substituting the value of \[\pi =\dfrac{22}{7}\], we get,
The volume of the cylinder \[=\left( \dfrac{22}{7} \right).\left( \dfrac{35}{2} \right)\left( \dfrac{35}{2} \right)\left( 120 \right)c{{m}^{3}}\]
\[=\left( 22 \right)\left( 5 \right)\left( 35 \right)\left( 30 \right)c{{m}^{3}}\]
\[=115500c{{m}^{3}}\]
We know that,
\[1\text{ }liter=1000c{{m}^{3}}\]
\[1c{{m}^{3}}=\dfrac{1}{1000}liters\]
So, we get,
\[115500c{{m}^{3}}=\dfrac{115500}{1000}=115.5liters\]
So, we get the capacity of the cylinder as 115.5 liters.

Note: In this question, many students make this mistake of substituting diameter in place of the radius which is wrong. They must properly read and convert the diameter into radius by halving if and then use it. Also, in any formula, all the dimensions must be of the same unit. So, first convert all the dimensions in the same unit as we took height and radius, both in cm and then use it to get the correct answer.