Question

Using reasoning, determine the number of marbles that you would expect to fit if you doubled the diameter (new diameter = 16 cm). Explain how you determined your answer.

Answer 1

To determine the number of marbles that would fit if you doubled the diameter, you can calculate the volume of the original and new spheres using the formula V = (4/3)πr³. The new sphere would hold approximately 8 times more marbles than the original sphere.

Step-by-step explanation:

To determine the number of marbles that would fit if you doubled the diameter, you need to understand the relationship between the diameter and the volume of a sphere. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. Since the diameter is doubled, the radius is also doubled. So, if the original diameter was 8 cm, the new diameter is 16 cm and the new radius is 8 cm.

Let's calculate the volume of the original and new spheres:

1. Original sphere: V = (4/3)π(4 cm)³ = 268.08 cm³
2. New sphere: V = (4/3)π(8 cm)³ = 2144.66 cm³

Therefore, we would expect the new sphere with a diameter of 16 cm to hold approximately 2144.66/268.08 = 8 times more marbles than the original sphere.