Respuesta :
Answer:
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 = [tex](\frac{x}{2})[/tex]
Formula to be used:
Surface area of the cube = [tex]6x^2[/tex] and Surface area of the sphere = [tex]4\pi (r)^2[/tex]
Volume of the cube = [tex]x^3[/tex] and Volume of the sphere = [tex]\frac{4\pi r^3}{3}[/tex]
We have to compare the ratio of SA and Volumes.
Ratio of SA : Ratio of their volumes :
⇒ [tex]\frac{SA\ of\ cube\ (S_1)}{SA\ of\ sphere\ (S_2)}[/tex] ⇒ [tex]\frac{Volume \ of \ cube\ (V_1)}{Volume\ of\ sphere\ (V_2)}[/tex]
⇒ [tex]\frac{6x^2}{4\pi (\frac{x}{2})^2}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi r^3}{3} }[/tex]
⇒ [tex]\frac{6x^2}{4\pi (\frac{x^2}{4})}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi (\frac{x}{2})^3}{3} }[/tex]
⇒ [tex]\frac{6x^2}{\pi x^2}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi (\frac{x^3}{8})}{3} }[/tex]
⇒ [tex]\frac{6}{\pi}[/tex] ⇒ [tex]\frac{6}{\pi}[/tex]
⇒ approx [tex]2[/tex] ⇒ approx [tex]2[/tex]
⇒ [tex]S_1=2S_2[/tex] ⇒ [tex]V_1=2V_2[/tex]
Packaging of the toy with the cube will be more efficient as it has more volume comparatively.
