Question

Find the volume of the balloon after 200200 sec.

a. V(200)=4/3π(50+0.05(200))^3
b. V(200)=4/3π(50−0.05(200))^3
c. V(200)=4/3π(50)^3+4π(50)^2(0.05(200))+4/3π(0.05(200))^3
d. V(200)=4/3π(50)^3+4π(50)(0.05(200))^2+4/3π(0.05(200))^3

Answer 1

The correct formula to find the volume of the balloon after 200200 seconds is V(200) = 4/3π(50 - 0.05(200200))^3.

Step-by-step explanation:

The formula for the volume of a balloon is given by V = 4/3πr³, where r is the radius of the balloon. In this case, the radius is given by 50 + 0.05(N), where N represents the number of seconds. Therefore, the correct formula to calculate the volume of the balloon after 200200 seconds is V(200) = 4/3π(50 + 0.05(200200))³. By simplifying the equation and calculating the expression in the brackets, we find that the correct answer is option b) V(200) = 4/3π(50 - 0.05(200200))³. This is because the expression inside the brackets represents the change in the radius of the balloon after 200200 seconds.