Question

A manufacturer plans to construct a cylindrical can to hold one cubic metre of liquid. If the cost of constructing the top and bottom is twice the cost of constructing the sides, what are the dimensions of the most economical can?

• A. $r=\frac{1}{{\left(2\pi \right)}^{1/3}},h={\left(\frac{4}{\pi }\right)}^{1/3}$
• B. $r=\frac{1}{{\left(\pi \right)}^{1/3}},h={\left(\frac{1}{\pi }\right)}^{1/3}$
• C. $r=\frac{1}{{\left(4\pi \right)}^{1/3}},h={\left(\frac{16}{\pi }\right)}^{1/3}$
• D. $r=\frac{1}{{\left(4\pi \right)}^{1/3}},h={\left(\frac{4}{\pi }\right)}^{1/3}$

Answer 1

The correct option is C $r=\frac{1}{{\left(4\pi \right)}^{1/3}},h={\left(\frac{16}{\pi }\right)}^{1/3}$