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