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 large ball is ? cubic inches larger than the 3 smaller balls.
To calculate the volume of a sphere, we use the formula V = (4/3)πr^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 = 4.19 * 9261
V_large = 38,799.39 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 = 4.19 * 64
V_small = 268.02 cubic inches
The total volume of the 3 small balls:
Total_volume_small = 3 * V_small
Total_volume_small = 3 * 268.02
Total_volume_small = 804.06 cubic inches
The difference in volume:
Difference = V_large - Total_volume_small
Difference = 38,799.39 - 804.06
Difference = 37,995.33 cubic inches
Therefore, the large ball is 37,995.33 cubic inches larger than the total volume of the 3 small balls.