Question
How much, larger, and volume, is one large ball that has a radius of 21 inches and the total volume of three balls that each have a radius of 4 inches?
Answers
Answered by
GPT 3.5
To calculate the volume of a sphere, we use the formula V = 4/3 * π * r^3, where r is the radius.
For the large ball with a radius of 21 inches:
V_large = 4/3 * π * (21)^3
V_large = 4/3 * π * 9261
V_large ≈ 38937.833 cubic inches
For each of the three smaller balls with a radius of 4 inches:
V_small = 4/3 * π * (4)^3
V_small = 4/3 * π * 64
V_small ≈ 268.083 cubic inches
Total volume of the three small balls:
V_total_small = 3 * V_small
V_total_small = 3 * 268.083
V_total_small = 804.249 cubic inches
Now we compare the volume of the large ball with the total volume of the three smaller balls:
V_large / V_total_small = 38937.833 / 804.249
V_large / V_total_small ≈ 48.437
Therefore, the large ball with a radius of 21 inches has a volume approximately 48.437 times larger than the total volume of the three smaller balls with a radius of 4 inches.
For the large ball with a radius of 21 inches:
V_large = 4/3 * π * (21)^3
V_large = 4/3 * π * 9261
V_large ≈ 38937.833 cubic inches
For each of the three smaller balls with a radius of 4 inches:
V_small = 4/3 * π * (4)^3
V_small = 4/3 * π * 64
V_small ≈ 268.083 cubic inches
Total volume of the three small balls:
V_total_small = 3 * V_small
V_total_small = 3 * 268.083
V_total_small = 804.249 cubic inches
Now we compare the volume of the large ball with the total volume of the three smaller balls:
V_large / V_total_small = 38937.833 / 804.249
V_large / V_total_small ≈ 48.437
Therefore, the large ball with a radius of 21 inches has a volume approximately 48.437 times larger than the total volume of the three smaller balls with a radius of 4 inches.