Answer:
The volume of the empty space is 20.57 unit³.
Step-by-step explanation:
Given,
The volume of the box = 96 cubic units,
Also, the cylindrical container is packed inside the box.
We know that,
The volume of a cylinder is,
\(V=\pi (r)^2 h\)
Where r is the radius of cylinder,
h is its height,
Here, r = \(\frac{4}{2}\) = 2 unit ( Radius = Diameter / 2 )
And, h = 6 units
Thus, the volume of the cylindrical container is,
\(V=\pi (2)^2(6)\)
\(=\frac{22}{7}\times 4\times 6 = \frac{528}{7}\text{ cubic unit}\)
Hence, the volume of the empty space between the cylinder and the box = Volume of the box - Volume of the container
\(= 96 - \frac{528}{7}\)
\(=\frac{672-528}{7}\)
\(=\frac{144}{7}=20.5714285714\approx 20.57\text{ cubic unit}\)
