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

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

$= 96 - \frac{528}{7}$

$=\frac{672-528}{7}$

$=\frac{144}{7}=20.5714285714\approx 20.57\text{ cubic unit}$

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