A right circular cylinder has fixed volume

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

V=100\pi\text{ cm}^3

. Write the ratio

R(r)=\dfrac{S}{V}

of its total surface area

S

to its volume in terms of its base radius

r

only, and find the value of

r

(in centimeters) that minimizes this ratio.