Question: you want to buy all three of the masks shown here. if sales tax is an additional 7% how much would you pay in total? (the masks cost 122.93)

$122.93
Add the 7% sales tax - which is $8.60

Total will be: $131.53

Differentiate implicitly. realize you want ds to be zero. .. ds = 2πr*dr + π*(dr*√(r^2+h^2) + r/(2√(r^2+h^2))*(2r*dr + 2h*dh)) .. 0 = dr*(2πr + π(√(r^2+h^2) + r^2/√(r^2+h^2)) + dh*(rh/√(r^2+h^2)) .. dr = -dh*(rh/√(r^2+h^2))/(2r + √(r^2+h^2) + r^2/√(r^2+h^2)) we could simplify more, or we could just plug in the numbers. let's do the latter. .. dr = -dh*(6*8/√(6^2+8^2))/(2*6 + √(6^2+8^2) + 6^2/√(6^2+8^2)) .. = -dh*(48/10)/(12 + 10 + 36/10) .. = -dh*(4.8/25.6) = -3*dh/16 if dh = 3/100, dr = (-3/16)*(3/100) = -9/1600 the estimated value of r is 6 cm less 9/1600 cm, about 5.994375 cm.