Cylindrical Steel Volume

Question

A cylindrical steel can is constructed so that its volume is exactly 2000cm³. What are possible assumptions? And relevant limitations?

 

a) What is the minimum possible area of steel that can be used? 

 

Answer 1

pi.r^2*h=2000

Assumptions

It is hollow cylinde and covered at both ends ,Thickness is is not making an impact on the volume .

limitations

so h,r>0

h*r^2=2000/pi

 

Area A=2*pi*r*h+2*pi*r^2

we know that

 pi*r*h=2000/r

 

So A=4000/r+2*pi*r^2

 

dA/dr=-4000/r^2+4*pi*r=0

 

4*pi*r^3=4000

r=10/(pi^(1/3))

 

d2A/dt2=+ ve

 

r=10/(pi^(1/3))== 6.8278 cm

h=2000/(pi*r*r)= 13.656 cm

 

A= 2*pi*r*(r+h)= 878.76 sq cm

Remember  If u assume that the cylinder is not covered  at both ends the solution lies at r=inf!!!!!!!!!!!!!!!!! A=0