Question

A cylindrical container is packaged inside a prism-shaped box. The box has a volume of 96 cubic units. If the container has a diameter of 4 units and a height of 6 units, what is the volume of the empty space between the cylinder and the box? Round the answer to two decimal places.

Answer 1

The volume of the empty space is 20.57 unit³.

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 =
`(4)/(2)` = 2 unit ( Radius = Diameter / 2 )

And, h = 6 units

Thus, the volume of the cylindrical container is,

`V=\pi (2)^2(6)`

`=(22)/(7)* 4* 6 = (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 - (528)/(7)`

`=(672-528)/(7)`

`=(144)/(7)=20.5714285714\approx 20.57\text{ cubic unit}`

Answer 2

Volume of container = π x 4^2 x 6/4 = 75.40 cubic units
volume of empty space = volume of box - volume of container = 96 - 75.40 = 20.60 cubic units