Question

would it not be more space and cost effective to package three squash balls in a cylindrical container rather than a rectangular box?

Answer 1

Answer:

Yes it would be more space and cost effective if it is cylindrical container rather than rectangular box.

Step-by-step explanation:

Let the radius of the squash balls be r

Then

If they are contained inside cylindrical container then the radius of base of the container will be r and height will be 6r

Volume of the container

$=\pi r^2\times6r$

$=6\pi r^3$ unit³

$=18.84r^3$ unit³

Total area of the material

$=\pi r^2+\pi r^2+2\pi r\times 6r$

$=2\pi r^2+12\pi r^2$

$=14\pi r^2$

$=43.98r^2$ unit²

If the balls are contained inside rectangular (cuboid) container then the length of the container will be 6r, while the breadth and height will be 2r

Volume of the container

$=6r\times2r\times 2r$

$=24r^3$ unit³

Total area of the material

$=2(6r\times 2r+2r\times 2r+6r\times 2r)$

$=2(12r^2+4r^2+12r^2)$

$=56r^2$ unit²

Since volume of cylindrical container is less than that of rectangular

The cylindrical container is more space effective

Also, since the area occupied by the material in the cylindrical container is less than that of rectangular

Therefore, the cylindrical container is more cost effective.

Hope this helps.