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. Round to the nearest hundredth.
First, calculate the volume of the large ball with a radius of 21 inches:
V_large = (4/3) * pi * 21^3
V_large = (4/3) * 3.14 * 9261
V_large = 12348.26 cubic inches
Next, calculate the total volume of the 3 small balls with a radius of 4 inches:
V_small = 3 * (4/3) * pi * 4^3
V_small = 3 * (4/3) * 3.14 * 64
V_small = 301.44 cubic inches
Now, find the difference in volume:
Difference = V_large - V_small
Difference = 12348.26 - 301.44
Difference ≈ 12046.82 cubic inches
Therefore, the large ball with a radius of 21 inches is approximately 12046.82 cubic inches larger in volume than the total volume of 3 small balls with a radius of 4 inches.