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?

1 Answer
Jul 10, 2016

see the explanation..

Explanation:

Height prop 1/(radius^2)

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

Now in next step when removing the proportional sign (prop) we use an equal to sign and multiply color(RED)"k" on either of the sides like this;

Height = k*1/(Radius^2)

{where k is constant (of volume)}

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

8 = k*1/4^2

8 * 4^2= k

8 * 16= k

k= 128

Now we have calculated our constant value color(red)"k" which is color(red)"128".

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

Height = k*1/(Radius^2)

2 = 128*1/r^2 {r is for radius}

r^2=128/2

r^2=64

sqrt(r^2) =sqrt 64

r = 8

Hence, for height of 2 cm with a constant of 128 we get the color(blue)(radius) of color(blue)(2 cm)