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.
wrong
wrong again please check your work
4/3 π*21^3 - 3*4/3 π * 4^3
= 4/3 π (21^3 - 3*4^3)
= 4/3 π (9261-192)
= 4/3 π * 9069
= 37988.138
The volume of a sphere is calculated using the formula V = (4/3) * pi * r^3, where r is the radius.
For the larger ball:
V_large = (4/3) * 3.14 * (21)^3
V_large = (4/3) * 3.14 * 9261
V_large = 39,141.72 cubic inches
For each of the smaller balls:
V_small = (4/3) * 3.14 * (4)^3
V_small = (4/3) * 3.14 * 64
V_small = 268.088 cubic inches
Total volume of 3 smaller balls:
V_total_small = 3 * V_small
V_total_small = 3 * 268.088
V_total_small = 804.264 cubic inches
Difference in volume:
Difference = V_large - V_total_small
Difference = 39,141.72 - 804.264
Difference = 38,337.456 cubic inches
Therefore, the larger ball is 38,337.456 cubic inches larger than the total volume of the 3 smaller balls.
Apologies for the error. Let's recalculate the correct values:
For the larger ball:
V_large = (4/3) * 3.14 * (21)^3
V_large = (4/3) * 3.14 * 9261
V_large = 1,257,341.64 cubic inches
For each of the smaller balls:
V_small = (4/3) * 3.14 * (4)^3
V_small = (4/3) * 3.14 * 64
V_small = 268.088 cubic inches
Total volume of 3 smaller balls:
V_total_small = 3 * V_small
V_total_small = 3 * 268.088
V_total_small = 804.264 cubic inches
Difference in volume:
Difference = V_large - V_total_small
Difference = 1,257,341.64 - 804.264
Difference = 1,256,537.376 cubic inches
Therefore, the larger ball is 1,256,537.376 cubic inches larger than the total volume of the 3 smaller balls.
Let's correct the calculation:
For the larger ball:
V_large = (4/3) * 3.14 * (21)^3
V_large = (4/3) * 3.14 * 9261
V_large = 38,912.04 cubic inches
For each of the smaller balls:
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:
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 = 38,912.04 - 804.27
Difference = 38,107.77 cubic inches
Therefore, the larger ball is 38,107.77 cubic inches larger than the total volume of the 3 smaller balls.
Thank you for providing the correction. The correct calculation is:
Volume of the larger ball:
V_large = (4/3) * 3.14 * (21)^3
V_large = (4/3) * 3.14 * 9261
V_large = 38,988.14 cubic inches
Volume of the three smaller balls combined:
V_three_smaller = 3 * ((4/3) * 3.14 * (4)^3)
V_three_smaller = 3 * ((4/3) * 3.14 * 64)
V_three_smaller = 3 * (268.09)
V_three_smaller = 804.27 cubic inches
Difference in volume:
Difference = V_large - V_three_smaller
Difference = 38,988.14 - 804.27
Difference = 38,183.87 cubic inches
Therefore, the larger ball is 38,183.87 cubic inches larger than the total volume of the three smaller balls.