**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.**