Question

The shape of a solid iron rod is cylindrical. Its height is 11 cm and base diameter is 7 cm. Then find the total volume of 50 such rods.

Answer 1

Hint: Volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object. We have a predefined formula for evaluating the volume of the cylinder. So, using this formula we can easily find the volume of 50 identical cylinders.

Complete step-by-step answer:
For our problem, we have a cylinder whose base diameter and height is given. It is casted to form 50 cylindrical rods.
So, the volume of the cylinder can be specified by the square product of radius with height and some constant.
This can be represented in mathematical expression as: $V=\pi {{r}^{2}}h$
where r be the radius and h be the height of the cylinder.
The cylinder has a diameter of 7 cm. So, the radius of the cylinder is $\dfrac{7}{2}cm$. The height of the cylinder is 11 cm.
So, the volume will be:
\[\begin{align}
  & = \dfrac{22}{7}\times \dfrac{7}{2}\times \dfrac{7}{2}\times 11 \\
 & =\dfrac{847}{2} \\
 & =423.5c{{m}^{3}} \\
\end{align}\]
Now, the volume of 50 such rods $=50\times 423.5=21175c{{m}^{3}}$.
Therefore, the volume of 50 solid iron cylindrical rods is 21175 cubic cm.

Note: The key step for solving this problem is the knowledge of volume of a cylinder. By using the suitable formula, the volume of the cylinder is evaluated without any error. This knowledge is useful in solving complex problems related to volume of a figure.