For its beef stew, Betty Moore Company uses aluminum containers that have the fo
ID: 2891458 • Letter: F
Question
For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders. Find the radius and height of a container if it has a capacity of 25 in.^3 and is constructed using the least amount of metal. (Round your answers to two decimal places.) radius in height in
For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders. Find the radius and height of a container if it has a capacity of 25 in.3 and is constructed using the least amount of metal. (Round your answers to two decimal places.) radius heightExplanation / Answer
let radius of cylinder =r , and its height is h
volume of cylinder,V=r2h =25in3
=>h=25/r2
surface area ,s=2r2+2rh
s=2r2+2r(25/r2)
s=2r2+(50/r)
least amount of metal means surface area is minimum
ds/dr=4r-(50/r2)
d2s/dr2=4+(100/r3)
for minimum surface area ds/dr=0,d2s/dr2>0
4r-(50/r2) =0
=>r3=(50/4)
=>r=(25/2)1/3
=>r=1.5846
d2s/dr2=4+(100/(50/4))
=>d2s/dr2=12 >0
h=25/r2,r=1.5846
=>h=25/1.58462
=>h=3.1692
the radius and height of a container if it has a capacity of 25 in.^3 and is constructed using the least amount of metal are
radius =1.58 in
height = 3.17 in
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