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.
The volume of a sphere is given by the formula V = (4/3) * pi * r^3, where r is the radius of the sphere.
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 = 4.19 * 9261
V_large = 38844.39 cubic inches
For each of the 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 = 4.19 * 64
V_small = 268.16 cubic inches
Total volume of 3 smaller balls:
V_total = 3 * V_small
V_total = 3 * 268.16
V_total = 804.48 cubic inches
Difference in volume:
Difference = V_large - V_total
Difference = 38844.39 - 804.48
Difference = 38039.91 cubic inches
Therefore, the larger ball is 38039.91 cubic inches larger than the total volume of the 3 smaller balls.