Question

Plz any one can help me with this question

Answer 1

Answer:

Step-by-step explanation:

Given the volume of the sphere expressed as V = 4/3πr³

If the balloon is being inflated so that the radius increases at a constant rate r(t) = 12t + 2, the function that represents the volume of the weather balloon in terms of time can be derived by simply substituting r = 12t+2 into the formula for finding the volume of the balloon as shown;

V(t) = 4/3 π(12t+2)³

V(t) = 4π(12t+2)³/3

b) To find the volume of the balloon 12 seconds after inflation begins, we will substitute t = 12 into the resulting equation in (a)

V(12) = 4π(12(12)+2)³/3

V(12) = 4π(144+2)³/3

V(12) = 4π(146)³/3

V(12) = 4π(3,112,136)/3

V(12) = 39,108,254.38/3

V(12) = 13,036,084.79

Volume of the balloon to neatest cube metres is 13,036,085m³