Final answer:
To find the percentage change in volume from cylinder A to cylinder B, we first calculated the volume of cylinder A to be 192π in³. Knowing that Cylinder B has a volume of 96π in³, we found the percentage change to be a decrease of 50%, which corresponds to option (a).
Step-by-step explanation:
To find the percentage change in volume from cylinder A to cylinder B, we must first calculate the volume of cylinder A. The volume of a cylinder is given by the formula V = πr²h. For cylinder A, we use a radius of 8 inches and a height of 3 inches to find its volume:
VA = π(8 in)²(3 in) = 64π in²(3 in) = 192π in³
Cylinder B has a volume of 96π in³. Now, we calculate the percentage change using the formula:
Percentage change = ((VB - VA) / VA) × 100%
Percentage change = ((96π in³ - 192π in³) / 192π in³) × 100% = (-96π in³ / 192π in³) × 100%
Percentage change = -50%
Thus, the volume decreases by 50%, so the correct answer is (a) 50% decrease.