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.
To calculate the volume of a sphere, you 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)π(21)^3
V_large = (4/3)(3.14)(9261)
V_large = 12348π cubic inches
For each of the three smaller balls with a radius of 4 inches:
V_small = (4/3)π(4)^3
V_small = (4/3)(3.14)(64)
V_small = 268.48π cubic inches
Therefore, the total volume of the three smaller balls is:
3 * V_small = 3 * 268.48π = 805.44π cubic inches
Now we can find the difference in volume between the large ball and the three smaller balls:
Difference = V_large - 3 * V_small
Difference = 12348π - 805.44π
Difference = 11542.56π cubic inches
So, the larger ball with a radius of 21 inches is approximately 11542.56π cubic inches larger in volume than the total volume of the three smaller balls with a radius of 4 inches each.