SOLUTION: A cylindrical can is to have volume 300 cubic centimetres. Find its height and its
radius if the total surface area (and hence the total amount of material used) is minimum.
[The
Algebra.Com
Question 233136: A cylindrical can is to have volume 300 cubic centimetres. Find its height and its
radius if the total surface area (and hence the total amount of material used) is minimum.
[The volume is given by V = r2h, and the surface area is S = 2rh + 2r2, where r is the
radius and h is the height.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A cylindrical can is to have volume 300 cubic centimetres. Find its height and its
radius if the total surface area (and hence the total amount of material used) is minimum.
[The volume is given by V = r2h, and the surface area is S = 2rh + 2r2, where r is the radius and h is the height.
:
Find h in terms of the Volume
= 300
h =
:
Surface area
S = +
Replace h with
S = +
we can cancel pi*r
S = +
S = +
:
Plot the equation :
With the help of a TI83, minimum on this graph: x=3.628, (Min SA ~ 248 sq/cm)
:
hence r = 3.628 cm is the radius
:
Find the height
h = = 7.255 cm is the height
:
:
Check this by finding the volume with this r and h
V =
V = 300.00
RELATED QUESTIONS
What is the radius and height of a cylinder if its volume is 1000 cubic centimetres? (answered by solver91311)
The volume of a cube is 8 cubic centimetres. Find its total surface... (answered by ewatrrr)
A right circular cylinder of radius r and height h has volume given by V=πr^2h and... (answered by ankor@dixie-net.com)
What is the surface area of a right circular cylindrical oil can, if the radius of its... (answered by macston)
THE VOLUME OF A CYLINDRICAL TANK IS GIVEN BY THE FORMULA V=pie h r^2 WHERE h IS THE... (answered by checkley75)
Hello tutors! Please help me with the question below :)
A cylindrical can of soup... (answered by josgarithmetic)
Please help me, tutors :)
A cylindrical can of soup has a volume of 170 cubic... (answered by josgarithmetic)
A common ant absorbs oxygen at a rate of about 6.2 mililiters per second per square... (answered by Theo,KMST)
A cylindrical soft drink can is to be constructed such that it will have a volume of 355... (answered by venugopalramana)
Hi! Thanks for answering my question:
A cylindrical container with a radius of 68cm... (answered by Edwin McCravy)