A toy company is considering a cube or sphere-shaped container for packaging a new product. The height of the cube would equal the diameter of the sphere . Compare the volume to surface area ratios of the containers. Which packaging will be more efficient? For a sphere, SA =4πr²

Packaging with cube will be more efficient.

Step-by-step explanation:

Given:

A cube and a sphere where the diameter of the sphere is equal to the height of the cube.

Let the height of the cube "x"

Radius of the sphere =  

Formula to be used:

Surface area of the cube = and Surface area of the sphere =

Volume of the cube = and Volume of the sphere =

We have to compare the ratio of SA and Volumes.

Ratio of SA :                                        Ratio of their volumes :

⇒                            ⇒

⇒                                           ⇒

⇒                                           ⇒

⇒                                               ⇒  

⇒                                                  ⇒

⇒ approx                                     ⇒  approx

⇒                                      ⇒

Packaging of the toy with the cube will be more efficient as it has more volume comparatively.