To the nearest tenth of a cubic inch, how much volume is added to a spherical balloon whose radius grows from 10 to 20 inches long?
well, the volume went from
4pi/3 * 10^3 = 4000pi/3
to
4pi/3 * 20^3 = 32000pi/3
Assuming you can evaluate those expressions, you should be able to answer the question
To find the volume added to the spherical balloon, we need to calculate the difference in volumes between the new and old radii.
The formula for the volume of a sphere is given by V = (4/3) * π * r^3, where V is the volume and r is the radius.
Let's calculate the volume of the balloon with a radius of 10 inches:
V1 = (4/3) * π * (10^3) = (4/3) * π * 1000 = 4188.79 cubic inches (rounded to the nearest hundredth).
Now, let's calculate the volume of the balloon with a radius of 20 inches:
V2 = (4/3) * π * (20^3) = (4/3) * π * 8000 = 33510.32 cubic inches (rounded to the nearest hundredth).
To find the volume added, we subtract the initial volume from the final volume:
V_added = V2 - V1 = 33510.32 - 4188.79 = 29321.53 cubic inches (rounded to the nearest hundredth).
Therefore, to the nearest tenth of a cubic inch, the volume added to the balloon is approximately 29321.5 cubic inches.