# The height of a cylinder with constant volume is inversely proportional to the square of its radius. If h = 8 cm when r = 4 cm, what is r when h = 2 cm?

To find the value of r when h = 2 cm, we can use the inverse proportionality relationship between the height and the square of the radius.

Let's denote the height as h and the radius as r. According to the given information, we know that the volume of the cylinder remains constant.

Using the inverse proportionality, we can write the equation as:

h ∝ 1/r^2

To solve for the constant of proportionality, we can substitute the given values into the equation:

8 ∝ 1/4^2

Simplifying this equation, we get:

8 ∝ 1/16

To find the constant of proportionality, we can multiply both sides of the equation by 16:

8 * 16 ∝ 1

128 ∝ 1

Now, we can use this constant of proportionality to find the value of r when h = 2 cm:

2 ∝ 1/r^2

Substituting the constant of proportionality, we have:

128 ∝ 1/r^2

To solve for r, we can rearrange the equation:

r^2 ∝ 1/128

Taking the square root of both sides, we get:

r ∝ 1/√128

Simplifying this expression, we have:

r ∝ 1/8√2

Therefore, when h = 2 cm, r is approximately equal to 1/8√2 cm.

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see the explanation..

This is what the above statement says about the inverse relationship between HEIGHT and SQUARE OF RADIUS.

{where k is constant (of volume)}

Putting the values of height and radius^2 we get;

Moving towards your question where radius is to be calculated. Plugging the values into the equation:

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