A cylinder whose height is two thirds of its diameter has the same volume as a sphere of radius 4 cm.

Given that

Height of the cylinder = 2/3 diameter

We know that

Diameter = 2(radius)

h = 2/3 × 2r = 4/3r

Volume of the cylinder=Volume of the sphere

$\pi r^{2} h=4 / 3 \pi r^{3}$

$\pi \times r^{2} \times(4 / 3 r)=4 / 3 \pi(4)^{3}$

$(r)^{3}=(4)^{3}$

r = 4 cm