Given:
The radius, r=4x
The height,

To find the volume of the cone:
The volume of the cone formula is,

Substitute the values of r and h in the above formula we get,

Hence, the volume of the cone is

Thus, the correct option is option D.
Answer:



Step-by-step explanation:
Given




Required
The dimension that minimizes the cost
The volume is:

This gives:

Substitute 


Make H the subject


The surface area is:
Area = Area of Bottom + Area of Sides
So, we have:

The cost is:



Substitute:
and 



To minimize the cost, we differentiate

Then set to 0


Rewrite as:

Divide both sides by W

Rewrite as:

Solve for 


Take cube roots

Recall that:







Hence, the dimension that minimizes the cost is:



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