mathematical question

abdullah:

a cylinder whose height is two third of its diameter has the same volume as a sphere of radius 4cm.calculate the one third radius of the cylinder

Let the diameter of the cylinder be 2x cm (The radius is x cm) the height of the cylinder is (4x/3) cm

The volume of the Cylinder = pi * x ² * h ==> pi * x ² * 4x/3 ==> 4pi*x ³ / 3

The volume of the sphere = 4 * pi * r ³ ==> 4 ⁴ * pi ==> 256pi

4pi*x ³ / 3 = 256pi

x ³ / 3 = 64

x ³ = 192

x = 192 ^1/3

x = 5.769 cm ( to 5 decimal places)

I don't know why you would want 1/3 of the radius but it is 5.769/3 = 1.923cm