Question

Find the volume of metal used in a solid cylinder of length 14 cm and diameter 10 cm.

Answer 1

Hint: The volume of the metal will be the volume of the cylinder. The formula for the volume of the cylinder is \[V=\pi {{r}^{2}}h\], with radius r and height h.

Complete step by step solution:
In the question, we are required to find the volume of metal used in a solid cylinder of length 14 cm and diameter 10 cm. The figure is as follows:

Now, since the cylinder formed with the metal is solid, so the volume of the cylinder will be the volume of metal required to build it.
Now, it is known that the volume of the cylinder with radius r and height h is given as \[V=\pi {{r}^{2}}h\].
Here, the diameter of the cylinder is given as 10 cm, so the radius (r) is half the diameter and will be 5 cm.
The height (h) of the cylinder is 14 cm. Here, the height will be the same as the length of the cylinder.
Thus, the volume of the cylinder is given as:
\[\begin{align}
  & \Rightarrow V=\pi {{r}^{2}}h \\
 & \Rightarrow V=\pi \times {{(5)}^{2}}\times 14 \\
 & \Rightarrow V=350\pi \\
\end{align}\]
So here the volume of the metal required will be the same as the volume of the cylinder, which will be \[350\pi \,\,c{{m}^{3}}\].

Note: When the cylinder is kept vertically then the circle base is downward. When the same cylinder is kept horizontally then the curved part will be at the bottom. The height of the cylinder in the first case will be the length of the same cylinder in the second case.