A spherical balloon has a 28-in. Diameter, when it is fully inflated half of the air, is let out of the balloon. Assume that the balloon remains a sphere.
a: Find the volume of the fully-inflated balloon.
b: Find the volume of the half-inflated balloon.
c: What is the radius of the half-inflated balloon?

a: V = 11494.04 in3

b: V_half = 5747.02 in3

c: r = 11.11 in

Step-by-step explanation:

The volume of a sphere is given by:

V = (4/3)*pi*r^3

Where r is the radius.

a: If the diameter is 28 in, the radius is 28/2 = 14 in, so the volume is:

V = (4/3)*pi*14^3 = 11494.04 in3

b: The volume of the half-inflated balloon will be half the volume of the fully-inflated balloon, so V_half = V/2 = 5747.02 in3

c: To find the radius of the half-inflated balloon we just need to use its volume in the formula:

5747.02 = (4/3)*pi*r^3

r^3 = 5747.02/(4pi/3) = 1372

r = 11.11 in