A beverage company must manufacture open-top cylindrical cups that hold exactly 355…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A beverage company must manufacture open-top cylindrical cups that hold exactly 355 cm

^3

of liquid. For such a cup, the derivative of the total material area with respect to the radius is

S'(r)=4\pi r-\frac{710}{r^{2}}.

Which value of

r

(in cm) will minimize the amount of material used? (a)

3.1\text{ cm}

(b)

5.6\text{ cm}

(c)

3.8\text{ cm}

(d)

7.5\text{ cm}