Question

A spherical balloon is being inflated and the radius of theballoon is increasing at a rate of 2 cm/s.(A) Express the radius (r) of the balloon as a function of thetime (t).(B) If V is the volume of the balloon as a function of theradius, find Vor and interpret it.

Answer 1

Answer:

A.) r = 2t

B.) V = 33.5t^3

Explanation:

Given that a spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s

A) Express the radius (r) of the balloon as a function of the time (t).

Since the rate = 2 cm/s that is,

Rate = radius/ time

Therefore,

2 = r/t

Make r the subject of formula

r = 2t

(B) If V is the volume of the balloon as a function of the radius, find V or and interpret it.

Let assume that the balloon is spherical. Volume of a sphere is;

V = 4/3πr^3

Substitute r = 2t into the formula

V = 4/3π(2t)^3

V = 4/3π × 8t^3

V = 32/3 × πt^3

V = 33.5t^3