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

Answer:

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)#