Now, let's design a cereal box with a different shape to see if the costs are lower! We will use a sphere. To do this, take the value for volume that you found in question 2 and plug it into the formula for the volume of a sphere (below). Solve for r, and feel free to use the cubic root function on this calculator

Question

Now, let's design a cereal box with a different shape to see if the costs are lower!  We will use a sphere.  To do this, take the value for volume that you found in question 2 and plug it into the formula for the volume of a sphere (below).  Solve for r, and feel free to use the cubic root function on this calculator 
1 point
Captionless Image
r = 3.57 inches
r = 4.05 inches
r = 6.02 inches

GPT 3.5 · Answer

Volume of a sphere formula: V = (4/3)πr^3

Given volume from question 2: V = 256π cubic inches

Now plug in the given volume into the formula:
256π = (4/3)πr^3

Solving for r:
r^3 = (3/4) * 256
r^3 = 192
r = ∛192
r ≈ 5.68 inches

Therefore, the radius of the sphere cereal box should be approximately 5.68 inches to achieve a volume of 256π cubic inches.