Question

Plz any one can help me with this question

USE A MODEL The volume V of a weather balloon with radius r is given by V(r) = 4

3

πr

3

. The balloon is being inflated


so that the radius increases at a constant rate r(t) = 1

2

t + 2, where r is in meters and t is the number of seconds since


inflation began.

a. Determine the function that represents the volume of the weather balloon in terms of time.

b. Find the volume of the balloon 12 seconds after inflation begins. Round your answer to the nearest cubic meter.

Answer 1

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