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 formula for the volume of a sphere is V = (4/3) * pi * r^3, where r is the radius of the sphere.
For 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 = 39,031.64 cubic inches
For 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
Total volume of 3 small balls:
V_total_small = 3 * V_small
V_total_small = 3 * 268.09
V_total_small = 804.27 cubic inches
Difference in volume:
Difference = V_large - V_total_small
Difference = 39,031.64 - 804.27
Difference = 38,227.37 cubic inches
Therefore, the larger ball is 38,227.37 cubic inches larger than the total volume of the 3 smaller balls.