Question

Suppose the shipping company were packing balls with a diameter of 2 inches instead of Cubes. Would the large box hold more balls or fewer balls than boxes? Explain your answer.

Answer 1

To determine if the larger box will hold more cubes or spheres, one should determine or calculate for the volumes of the figures and whichever gives the smaller value will have to be the answer.

Volume of cube = (edge)³ = (2 in)³ = 8 in³

Volume of sphere = (4πr³)/3
where r is the radius and is equal to half of the length of the sides. Substituting,
Volume of sphere = (4π)(1 in)³ / 3 = 4.19 in³

Since spheres give the smaller value for volume, the answer to this item would have to be SPHERE.