How much larger, in volume, is one large ball that has a radius of 21 inches than the total volume of 3 balls that each have a radius of 4 inches? Use 3.14 for pi.
First, calculate the volume of the large ball with a radius of 21 inches:
V_large = (4/3) * 3.14 * (21^3)
V_large = (4/3) * 3.14 * 9261
V_large = 4.19 * 9261
V_large = 38841.39 cubic inches
Next, calculate the volume of each small ball with a radius of 4 inches:
V_small = (4/3) * 3.14 * (4^3)
V_small = (4/3) * 3.14 * 64
V_small = 268.09 cubic inches
Now, calculate the total volume of the 3 small balls:
Total_volume_small = 3 * V_small
Total_volume_small = 3 * 268.09
Total_volume_small = 804.27 cubic inches
Finally, calculate how much larger the volume of the large ball is than the total volume of the small balls:
Difference = V_large - Total_volume_small
Difference = 38841.39 - 804.27
Difference = 38037.12 cubic inches
Therefore, the volume of the large ball with a radius of 21 inches is 38,037.12 cubic inches larger than the total volume of the 3 small balls with a radius of 4 inches.