Question

What is the volume of a right rectangular prism with sides of 12cm, 3cm, and 3cm?

Answer 1

Hint: The equation to find the volume of a right rectangular prism given the required dimensions, is, $Volume=lbh$ , where l denotes length of the prism, b denotes breadth of the prism and h denotes the height of the prism. Using the values given and this equation, we can find the volume of the right rectangular prism.

Complete step by step answer:
In the question, we have been given the sides or the dimensions of the prism as 12cm, 3cm, and 3cm respectively. A right rectangular prism is a solid which has rectangles as its bases and is covered by rectangles on 4 sides. In other words, it is a cuboid. It is as shown in the figure.

The volume of a solid is defined as the amount of space inside or enclosed by the solid. It is dependent on all the three of its dimensions, namely, length, breadth and height. The formula for the volume of a right rectangular prism is given by $Volume=lbh$. From the question and the figure, we have length as 3cm, breadth as 3cm and height as 12cm, therefore substituting these values to find volume we get,
$\begin{align}
  & \,\,\,\,\,\,Volume=3cm\times 3cm\times 12cm \\
 & \Rightarrow Volume=108\,c{{m}^{3}} \\
\end{align}$
Therefore, we have found the volume of the right rectangular prism to be $108\,c{{m}^{3}}$.

Note: Another way to find volume of any regular prism is by finding the base area first and then multiplying it with the height. Base area can be found by,
$\begin{align}
  & \,\,\,\,\,\,Area=lb \\
 & \Rightarrow Area=3cm\times 3cm \\
 & \Rightarrow Area=9c{{m}^{2}} \\
\end{align}$
Next, we multiply it with the height to find volume.
$\begin{align}
  & \,\,\,\,\,\,Volume=Area\times h \\
 & \Rightarrow Volume=9c{{m}^{2}}\times 12cm \\
 & \Rightarrow Volume=108c{{m}^{3}} \\
\end{align}$
Hence, the volume of the prism is $108\,c{{m}^{3}}$.