SOLUTION: a cylindrical tin of particular volume is to be made using as little material as possible. find the ratio of the height to the radius(the tin is closed both ends)

Question 61016This question is from textbook as pure mathematics
: a cylindrical tin of particular volume is to be made using as little material as possible. find the ratio of the height to the radius(the tin is closed both ends) This question is from textbook as pure mathematics

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
a cylindrical tin of particular volume is to be made using as little material as possible. find the ratio of the height to the radius(the tin is closed both ends)
LET THE RATIO OF HEIGHT TO RADIUS = X =H/R.....H=RX
VOLUME OF CYLINDER = PI*(R^2)*H = V = CONSTANT.
V = PI*R^2*RX = PI*(R^3)*X
R=[V/(PI*X)]^(1/3)
A = AREA OF CYLINDER = 2PI*R*H+2PI*R^2=2PI*R[RX+R]=2PI*(R^2)[X+1]
A = 2PI*R^2[X+1]=2PI[X+1][V/(PI*X)]^(2/3)
A=[2PI*V^(2/3)/{PI}^(2/3)][(X+1)/X^(2/3)]
A = K[X^(1/3)+X^(-2/3)]
DA/DX = 0 FOR MINIMUM VALUE = K[(1/3){X^(-2/3)} -(2/3){X^(-5/3)}]=0
1/3{X^(2/3)}= 2/3{X^(5/3)}
X^(5/3)/X^(2/3)=2
X = 2

RELATED QUESTIONS
A cylindrical container is to have a volume of 100 pi square inches. (answered by josgarithmetic)

In a particular type of alloy the ratio of lead to tin is 5 : 6. The amount of lead... (answered by richwmiller)

Hi, can you help me with this problem? A storage bin for corn consists of a... (answered by ankor@dixie-net.com)

A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by (answered by solver91311)

A cylindrical biscuit tin has a close-fitting lid which overlaps the tin by 1cm. The... (answered by KMST)

A company that manufactures dog food wishes to pack in closed cylindrical tins. What... (answered by ikleyn,greenestamps,Edwin McCravy,MathLover1)

A rectangular box with square base and a fixed volume (V) is to be made from two types of (answered by Fombitz)

a closed cylindrical tin is required to contain 500cc show that an equation for the... (answered by Cromlix)

Information: A rectangular box which is open at the top, has a square base with sides of... (answered by josgarithmetic)