Question

A milk tank in the form of a cylinder, whose radius is \[1.5\] m and length is 7 m. Find the volume of the tank.

Answer 1

Hint: Here, we have to find the volume of the tank. We will use the volume of the cylinder to find the volume of the tank. We will substitute the given values in the formula and simplify it to find the required answer. Volume is a quantity of three-dimensional space enclosed by a closed surface.

Formula Used:
Volume of a cylinder is given by the formula \[V = \pi {r^2}h\] where \[r\] is the radius of the cylinder and \[h\] is the height of the cylinder.

Complete Step by Step Solution:
Here, the length of the cylinder is equal to the height of the cylinder.
So, we will first draw the diagram based on the information given in the question.

We have Radius of a cylinder, \[r = 1.5m\] and Height of the Cylinder, \[h = 7m\].
Substituting \[r = 1.5m\] and \[h = 7m\] in the formula \[V = \pi {r^2}h\], we get
Volume of tank\[ = \pi \times {(1.5)^2} \times 7\]
We know that \[\pi = \dfrac{{22}}{7}\] is a constant. So,
\[ \Rightarrow \] Volume of tank\[ = \dfrac{{22}}{7} \times {(1.5)^2} \times 7\]
Multiplying the terms, we get
\[ \Rightarrow \] Volume of tank\[ = 22 \times {(1.5)^2}\]
Squaring the term, we get
\[ \Rightarrow \] Volume of tank\[ = 22 \times 2.25\]
Multiplying the terms, we get
\[ \Rightarrow \] Volume of tank \[ = 49.5\]

Therefore, the volume of the tank is \[49.5{m^3}\].

Note:
In order to solve this question we need to remember the formula of volume of the cylinder. We might make a mistake by using the formula as \[V = 2\pi rh\] instead of \[V = \pi {r^2}h\]. \[V = 2\pi rh\] will give us the area of the cylinder and not its volume. The volume of a cylinder is the density of the cylinder that signifies the amount of material it can carry or how much amount of any material can be immersed in it.