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 volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.
For the large ball with a radius of 21 inches:
V1 = (4/3) * 3.14 * 21³
V1 = (4/3) * 3.14 * 9261
V1 = 39.48 * 9261
V1 = 365,759.88 cubic inches
For each of the smaller balls with a radius of 4 inches:
V2 = (4/3) * 3.14 * 4³
V2 = (4/3) * 3.14 * 64
V2 = 4.19 * 64
V2 = 268.16 cubic inches
The total volume of the 3 smaller balls is:
3 * V2 = 3 * 268.16
3 * V2 = 804.48 cubic inches
Therefore, the difference in volume between the large ball and the total volume of the 3 smaller balls is:
365,759.88 - 804.48
365,759.88 - 804.48 = 364,955.40 cubic inches
The large ball is 364,955.40 cubic inches larger in volume than the total volume of the 3 smaller balls.