Answer:
the dimension that will minimize cost are radius of 2.79 inch and height of cylinder of 1.40 inch.
Step-by-step explanation:
volume of a circular cylinder = πr²h
volume of 19 fluid ounces (1 fluid ounce is approximately 1.80469 cubic inches) = 19* 1.80469 =34.28911 in³
The cost per square inch of constructing the top and bottom is twice the cost of constructing the lateral side, means
surface area of top + bottom = surface area of side
area of circle(top + bottom) = πr²+πr² = 2πr²
area of the side = 2πrh
the cost of top and bottom = twice the cost of side
2πr² = 2( 2πrh) = 4πrh
divide both side by 2πr
r= 4πrh/ 2πr =2h
r = 2h
for volume = πr²h = 34.28911 in³
and r = 2h
π(2h)²h =34.28911 in³
4πh³ = 34.28911 in³
h³ = 34.28911 /(4*3.142) = 2.7283 in³
h = cube root of 2.7283 in³ = 1.397 inch
r = 2* 1.76 = 2.794 inch
the dimension that will minimize cost are radius of 2.79 inch and height of cylinder of 1.40 inch.
