The surface area of a cylindrical can is equal to the sum of the area of two circles and the body of the cylinder: 2πr2 + 2πrh. volume is equal to π<span>r2h.
V = </span>π<span>r2h = 128 pi r2h = 128 h = 128/r2
A = </span><span>2πr2 + 2πrh </span>A = 2πr2 + 2πr*(<span>128/r2) </span>A = 2πr2 + 256 <span>π / r </span><span> the optimum dimensions is determined by taking the first derivative and equating to zero.
dA = 4 </span>πr - 256 <span>π /r2 = 0 r = 4 cm h = 8 cm </span><span>
