25 pointsa cone has height h and a base with radius r. you want to change the cone so it's volume is tripled. what is the new height if you only change the height? what is the new radius if you only change the radius? explain.

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.