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. Click HERE for Help video. (10 points)
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.
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 = 12.56 * 9261
V_large ≈ 116,264.16 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 = 4.187 * 64
V_small ≈ 268.42 cubic inches
Total volume of 3 smaller balls:
3 * V_small = 3 * 268.42
Total volume = 805.26 cubic inches
Difference in volume:
116,264.16 - 805.26 ≈ 115,458.9 cubic inches
Therefore, the larger ball is approximately 115,458.9 cubic inches larger than the total volume of the 3 smaller balls.
wrong
Let's calculate it correctly.
Volume of the large ball with radius 21 inches:
V_large = (4/3) * pi * r^3
V_large = (4/3) * 3.14 * 21^3
V_large = (4/3) * 3.14 * 9261
V_large = (4/3) * 3.14 * 804357
V_large = 3815.19 cubic inches
Volume of each small ball with radius 4 inches:
V_small = (4/3) * pi * r^3
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 smaller balls:
3 * V_small = 3 * 268.09
Total volume = 804.27 cubic inches
Difference in volume:
3815.19 - 804.27 = 3010.92 cubic inches
Therefore, the larger ball is 3010.92 cubic inches larger than the total volume of the 3 smaller balls.