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.
The larger ball is ____ cubic inches larger than the 3 smaller balls.
To find the volume of a sphere, we use the formula V = (4/3) * pi * r^3
For the larger ball with a radius of 21 inches:
V_large = (4/3) * 3.14 * (21)^3
V_large = (4/3) * 3.14 * 9261
V_large = 12348 * 3.14
V_large = 38786.32 cubic inches
For each of the 3 smaller balls with a radius of 4 inches:
V_small = (4/3) * 3.14 * (4)^3
V_small = (4/3) * 3.14 * 64
V_small = 33.49 cubic inches
Total volume of the 3 smaller balls:
Total_small = 3 * V_small
Total_small = 3 * 33.49
Total_small = 100.47 cubic inches
Difference in volume:
Difference = V_large - Total_small
Difference = 38786.32 - 100.47
Difference = 38685.85 cubic inches
Therefore, the larger ball is 38685.85 cubic inches larger than the 3 smaller balls.