Final answer:
The volume of the weather balloon after 1 minute can be found by integrating the rate function r(t) = 18(1 - 2t)^2 from t = 0 to t = 60 seconds. After performing the integration and the calculations, the total volume in liters will be obtained.
Step-by-step explanation:
The question asks to find the volume of a weather balloon after 1 minute when the balloon is being filled at a certain rate. The rate at which the balloon is being filled is given by the function r(t) = 18(1 - 2t)^2, where t is the time in seconds. To find the volume after 1 minute, which is 60 seconds, we need to integrate the rate function from t = 0 to t = 60.
Performing the integration, we get:
V(t) = ∫ r(t) dt
V(t) = ∫ 18(1 - 2t)^2 dt
V(t) = 18 ∫ (1 - 4t + 4t^2) dt
V(t) = 18 [t - (4/2)t^2 + (4/3)t^3] from 0 to 60
V(t) = 18 [60 - 2(60^2) + (4/3)(60^3)]
After performing the calculations, we will get the total volume of the balloon after 1 minute.