Math question and I need urgent help

Question

A food manufacturer wants to find the most efficient packaging for a canister of oatmeal with a volume of 1663 cubic centimeters.

a. Use the formula for the volume of a cylinder to write an equation that gives the height h of a possible canister in terms of its radius r.

b. Write an equation that gives the canister's surface area S in terms of its radius r by substituting the expression for h from part (a) into the formula for the surface area of a cylinder.

c. Graph the equation from part (b) using desmos.

What are the dimensions that use the least material (round to one decimal)? r = _____cm      h ____= cm

Answer 1

a)

 

πr²h = 1663

 

Solving for h,

 

h = 1663 / (πr²)

 

 

b)

 

S = 2πr² + 2πr(1663 / πr²)

S = 2πr² + (3326/r)

 

 

c)

 

Input the function in desmos:

 

y = 2πx² + (3326/x)

 

 

d)

 

Find the minimum point on the curve from desmos.