<p>A small conic container holds 4 mL of liquid. What should be the radius be if the goal of the design is to minimize the amount of material used for the lateral surface? </p>
<p>Can the answer be a number? Is it possible to solve for r without the height? </p>
<p>I’m not sure if I’m qualified to answer this because I’m still a prospie, but I recall doing similar questions for A Levels. Here’s how I would solve it:</p>
<p>Try using the volume to get an equation between r and h:
4 = π<em>r^2</em>h/3
subject h:
h = 12/(π*r^2) --------(1)</p>
<p>Then write the expression for surface area (=amount of material used):
S = πr^2 + πr*sqrt(r^2 + h^2) ----------(2)</p>
<p>Use (1) in (2) to eliminate the h term. Now you have an expression for the surface area purely in terms of r. To find a minimum value of r, graph this equation or use d(S)/dr=0.</p>
<p>Hope this helps!</p>
<p>Edit: Pay careful attention to units! You may need to convert 4mL into cubic meters.</p>
<p>Okay that makes good sense! Thank you so much!! </p>