Question

Find the volume of the below figure:

Answer 1

Hint: As you can see that the given figure is a cuboid so basically, we have to find the volume of the cuboid having a length, breadth, and height of 1.6 cm, 4 mm, and 1.1 cm respectively. We know that if the length, breadth, and height of the cuboid are equal to l, b and h then the volume corresponding to that dimension of the cuboid is equal to $l\times b\times h$. Now, substitute the values of length, breadth, and height given in the above problem and solve this multiplication.

Complete step-by-step solution:
The cuboid of which we have to find the volume is given as:

In the above figure, the dimensions of the cuboid are given as follows:
The length of the cuboid is equal to:
$1.6cm$
Breadth of the cuboid is equal to:
$4mm$
Height of the cuboid is equal to:
$1.1cm$
We know that volume of the cuboid having length, breadth and height as l, b and h respectively is equal to:
$l\times b\times h$
In the above formula, the units of l, b and h should be same but in the above question only the units of breadth is in mm but the units of length and height are given in cm so we are going to convert the units of breadth into cm as follows:
Breadth $=4mm$
We know that,
$10mm=1cm$
Dividing 10 on both the sides we get,
$\begin{align}
  & \dfrac{10}{10}mm=\dfrac{1}{10}cm \\
 & \Rightarrow 1mm=\dfrac{1}{10}cm \\
\end{align}$
Multiplying 4 on both the sides we get,
$\begin{align}
  & 4mm=\dfrac{4}{10}cm \\
 & \Rightarrow 4mm=0.4cm \\
\end{align}$
Hence, we have converted 4mm into 0.4cm.
Now, substituting the value of l as 1.6 cm, b as 0.4 cm and h as 1.1 cm in the formula of volume of the cuboid we get,
$\begin{align}
  & l\times b\times h \\
 & =1.6\times 0.4\times 1.1c{{m}^{3}} \\
 & =0.704c{{m}^{3}} \\
\end{align}$
Hence, we got the volume of the cuboid as $0.704c{{m}^{3}}$.

Note: We have converted the units of breadth which is mm into cm, instead of doing this you can convert the units of length and height into mm and keep the unit of breadth remains same which we have shown below:
Length is given as 1.6 cm so converting this unit into mm we get,
$1cm=10mm$
Multiplying 1.6 on both the sides we get,
$\begin{align}
  & 1.6cm=10\left( 1.6 \right)mm \\
 & \Rightarrow 1.6cm=16mm \\
\end{align}$
Now, converting units of height which is 1.1 cm into mm we get,
$\begin{align}
  & 1.1cm=10\left( 1.1 \right)mm \\
 & \Rightarrow 1.1cm=11mm \\
\end{align}$
Now, the volume of the cuboid in $m{{m}^{3}}$ is equal to:
$\begin{align}
  & 16\times 4\times 11m{{m}^{3}} \\
 & =704m{{m}^{3}} \\
\end{align}$
Hence, we got the volume of cuboid as $704m{{m}^{3}}$.
In the above solution, we have converted the only breadth into cm because the majority of the dimensions are in cm and it will reduce the time to solve questions. You can write the volume in $m{{m}^{3}}$ also unless it is specified that you have to find the volume in $c{{m}^{3}}$.