A cylindrical can has height h and radius r both measured in cm. If the rate of increase of volume of the can with respect to height equals the rate of increase of volume with respect to radius, what is the relationship between height and radius

Respuesta :

Answer:

It simply means that the radius is directly proportional to the height.

The relationship between the height and radius is R = 2H.

Relationship between height & radius:

Let us assume the radius be Rand height be H

Since the rate of increase of the volume with regard to the height should be equivalent to the rate of increase of volume with respect to the radius

Now we know that the volume = [tex]\pi R^2H[/tex]

So,

[tex]V/H = V/R\\\\\pi R^2 = \pi R^2H\\\\R = 2H[/tex]

Therefore, The relationship between the height and radius is R = 2H.

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