Question

The height of the cylinder is 6cm and the base area is \[5c{{m}^{2}}\]. What is the volume of a cylinder?

Answer 1

Hint: So as we know that volume of cylinder is \[\pi {{r}^{2}}h\] in which $\pi $ is constant, ‘r’ is radius of cylinder and ‘h’ is the height of cylinder. Since in our question we had height of cylinder and area of base, so as we know that base area of cylinder is \[\pi {{r}^{2}}\] which is further multiplied by height of cylinder to have h volume of cylinder. So we will go with this to find the volume of the cylinder.

Complete step by step solution:

So moving ahead with the question, in step-to-step manner, as according to question we know that;
Height of cylinder is $=6cm$
Base area of cylinder is $=5c{{m}^{2}}$
We want to know the volume of cylinder,
As we know that volume of cylinder is \[=\pi {{r}^{2}}h\]
Which we got when the base area of the cylinder is multiplied with the height of the cylinder. So from here we can say that if the base area of the cylinder is multiplied with the height of the cylinder then we will get the volume of the cylinder. So we can write it as;
Volume of cylinder $=$ base area of cylinder $\times $ height of cylinder
Since we know the value of base area and height of cylinder, as given in question, so put them in above equation;
 \[\begin{align}
  &\text{Volume of cylinder}=\text{Base area of cylinder}\times \text{Height of cylinder} \\
 & \text{Volume of cylinder}=\left( 6cm \right)\times \left( 5c{{m}^{2}} \right) \\
\end{align}\]
So solving it further we will get;
\[\begin{align}
  &\text{Volume of cylinder}=\left( 6cm \right)\times \left( 5c{{m}^{2}} \right) \\
 &\text{Volume of cylinder} =30c{{m}^{3}} \\
\end{align}\]
So from here we can say that the volume of the cylinder is \[30c{{m}^{3}}\].
Hence the answer is \[30c{{m}^{3}}\].

Note: For solving the type of question you need to go through the area/volume formula of different figures which are common, for example rectangle, square, cube, cylinder, sphere, hemi sphere and so on. Moreover keep noted that you need to clearly specify the unit, as volume has cubic unit, square has quadratic unit as we have\[c{{m}^{3}}\]and\[c{{m}^{2}}\] respectively.