Question

what is the volume of the rectangular box? and which box is a better fit and wastes less space for the Rubiks ball

Answer 1

Given:

The dimension of the spherical ball is a diameter of 4in. That is the radius,

`r=2in`

The dimensions of the cylinder are,

`\begin{gathered} Radius,r=2in \\ Height,h=4in \end{gathered}`

The dimensions of the rectangular are

`\begin{gathered} Length,l=4in \\ Breadth,b=4in \\ Height,h=4in \end{gathered}`

To find:

The option which has less waste place.

Step-by-step explanation:

The volume of the sphere is,

`\begin{gathered} V=(4)/(3)\pi r^3 \\ =(4)/(3)*(22)/(7)*2^3 \\ =33.52in^3 \end{gathered}`

The volume of the cylinder is,

`\begin{gathered} V=\pi r^2h \\ =(22)/(7)*2^2*4 \\ =50.29in^3 \end{gathered}`

The volume of the rectangle is,

`\begin{gathered} V=lbh \\ =4*4*4 \\ =64in^3 \end{gathered}`

After fitting the spherical ball in the cylinder box, the remaining waste place will be,

`50.29-33.52=16.77in^3...........(1)`

After fitting the spherical ball in the rectangular box, the remaining waste place will be,

`64-33.52=30.48in^3.........(2)`

Comparing (1) and (2), we get to know that the cylinder will have less waste place.

Final answer:

Option 1 - cylinder