Answer:
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.
Step-by-step explanation:
Given that, the volume of cylindrical can with out top is 25 cm³.
Consider the height of the can be h and radius be r.
The volume of the can is V=
According to the problem,
The surface area of the base of the can is =
The metal for the bottom will cost $2.00 per cm²
The metal cost for the base is =$(2.00× )
The lateral surface area of the can is =
The metal for the side will cost $1.25 per cm²
The metal cost for the base is =$(1.25× )
Total cost of metal is C= 2.00 +
Putting
Differentiating with respect to r
Again differentiating with respect to r
To find the minimize cost, we set C'=0
⇒r=1.71
Now,
When r=1.71 cm, the metal cost will be minimum.
Therefore,
⇒h=2.72 cm
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.