Question
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. Round to the nearest hundredth. Click HERE for Help video. (1 point)
The larger ball is 38039.91 cubic inches larger than the 3 smaller balls.
To find the volume of the large ball with a radius of 21 inches, we use the formula for the volume of a sphere: V = (4/3)πr^3
V_large = (4/3) * π * (21)^3
V_large = (4/3) * 3.14 * 9261
V_large = 12.56 * 9261
V_large = 116301.36 cubic inches
Next, we find the total volume of the 3 smaller balls with a radius of 4 inches each:
V_small = 3 * (4/3) * π * (4)^3
V_small = 3 * (4/3) * 3.14 * 64
V_small = 12 * 3.14 * 64
V_small = 2419.52 cubic inches
Finally, we find the difference in volume between the large ball and the 3 smaller balls:
Difference = V_large - V_small
Difference = 116301.36 - 2419.52
Difference = 113881.84 cubic inches
Rounded to the nearest hundredth, the larger ball is 113881.84 cubic inches larger than the 3 smaller balls.
wrong
My apologies for the error. Let's try again:
To find the volume of 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 = 12.56 * 9261
V_large = 116308.16 cubic inches
To find the volume of each small ball with a radius of 4 inches:
V_small = (4/3) * π * 4^3
V_small = (4/3) * 3.14 * 64
V_small = 268.09 cubic inches
Since there are 3 small balls, the total volume of the small balls is:
Total V_small = 3 * V_small
Total V_small = 3 * 268.09
Total V_small = 804.27 cubic inches
Now, let's find the difference in volume:
Difference = V_large - Total V_small
Difference = 116308.16 - 804.27
Difference = 115503.89 cubic inches
Rounded to the nearest hundredth, the larger ball is 115503.89 cubic inches larger than the 3 smaller balls.