Answer:
The volume of a balloon is directly proportional to the cube of its radius, so we can use the formula:
V1/V2 = (R1/R2)^3
Where V1 is the initial volume, V2 is the final volume, R1 is the initial radius, and R2 is the final radius. We know that when the radius is 4 inches, the volume is 192 cubic inches, so we can use this information to find the final volume when the radius is 3 inches.
V1 = 192 cubic inches
R1 = 4 inches
R2 = 3 inches
V1/V2 = (R1/R2)^3
V2 = V1 / (R1/R2)^3
V2 = 192 / (4/3)^3 = 192/ (4/27) = 192 * 27/4 = 192 * 6.75 = 1296 cubic inches
So, 1296 cubic inches of gas must be released to reduce the radius down to 3 inches.