The radius of the base of the cylinder is 2x cm and the height of the cylinder is h cm. The radius of the sphere is 3x cm.
The volume of the cylinder is equal to the volume of the sphere.
Express h in terms of x. Give your answer in its simplest form.

h = 9x

Step-by-step explanation:

Given: i. for the cylinder, base radius = 2x cm, height = h cm

           ii. for the sphere, radius = 3x cm

           iii.  volume of the cylinder = volume of the sphere

volume of a cylinder is given as;

volume = h

where: r is its base radius and h the height

volume of the given cylinder = x x h

                                              = x 4 x h

                                              = h

volume of a sphere =

where r is the radius.

volume of the given sphere =   x

                                         =   x 9

                                         = 12

Since,

volume of the cylinder = volume of the sphere

Then we have;

h = 12

4 h = 36

subtract from both sides

4h = 36x

divide both sides by 4

h =

  = 9x

h = 9x

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gregory's graph is incorrect because it shows 2 inches of growth for each week when it should show 0.75 inches of growth each week.