Question

A soup can is in the shape of a right cylinder. The can has a volume of 16 fluid ounces. The height is three times its radius. The metal used to make the lateral surface of the can costs $0.01 per square inch. The metal used to make the top and bottom costs $0.02 per square inch. If one fluid ounce is approximately 1.805 cubic inches, what is the total cost to make one empty soup can? Use 3.14 for straight pi

Answer 1

Answer:

$0.662772

Explanation:

v = Volume of can = 16 fl oz.

$1\ floz.=1.805\ in^3$

r = Radius of can

h = Height of can = 3r

Volume of cylinder is given by

$\pi r^2h=16\times 1.805\\\Rightarrow \pi r^23r=16\times 1.805\\\Rightarrow 3\pi r^3=16\times 1.805\\\Rightarrow r=\left(\frac{16\times 1.805}{3\times 3.14}\right)^{\frac{1}{3}}\\\Rightarrow r=1.45247\ in$

h=3r\\\Rightarrow h=3\times 1.45247\\\Rightarrow h=4.35741\ in[/tex]

Surface area of sides is given by

$2\pi rh\\ =2\times 3.14\times 1.45247\times 4.35741\\ =39.76632\ in^2$

Surface area of top and bottom is given by

$2\pi r^2\\ =2\times 3.14\times 1.45247^2\\ =13.25544\ in^2$

Cost of making the can will be

$39.76632\times 0.01+13.25544\times 0.02=\ 0.662772$

The cost to make the can is $0.662772