Final answer:
To find out how many 1 cm³ cubes can be formed from a spherical ball with a 21 cm diameter, calculate the sphere's volume and divide by the volume of one cube. The correct number of 1 cm³ cubes obtained is 4,849, which does not match any of the provided options.
Step-by-step explanation:
The question asks about converting the volume of a spherical ball into several small cubes and determining the number of cubes formed. To find the answer, we first need to calculate the volume of the sphere using its diameter, and then calculate how many 1 cm³ cubes can be formed from that volume.
The formula for the volume of a sphere is V = 4/3 πr³, where r is the radius of the sphere. Given that the sphere has a diameter of 21 cm, the radius r is half of the diameter, which is 10.5 cm. Thus, the volume of the sphere is:
V = 4/3 π(10.5 cm)³ ≈ 4,849 cm³
Each small cube has a volume of 1 cm³ (since all sides are 1 cm in length), so we can calculate the number of cubes by dividing the total volume of the sphere by the volume of one cube:
Number of cubes = Total volume of sphere / Volume of one cube = 4,849 cm³ / 1 cm³ = 4,849
Therefore, the answer is none of the provided options (a, b, c, or d).