Total volume = Volume of Sphere + Volume of Cylinder 16 = (4/3)πr³ + πr²h Express h in terms of r: πr²h = 16 - (4/3)πr³ h = 16/πr² - (4/3)r
Next, let's solve for surface area:
Total Surface Area = SA of sphere + SA of cylinder A = 4πr² + 2πrh Substitute the expression for h: A = 4πr² + 2πr[16/πr² - (4/3)r] A = 4πr² + 32/r - (8/3)πr²
Find the derivative of A with respect to r and equate to zero.