A cylinder whose height is two thirds of its diameter, has the same vo

1.	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.
Answer» Radius of a sphere (R)= 4 cm Height of the cylinder = \(\frac{2}{3}\) diameter We know, Diameter = 2(Radius) Let h be the height and r be the base radius of a cylinder, then h = \(\frac{2}{3}\) x (2r) = \(\frac{4r}{3}\) Volume of the cylinder = Volume of the sphere πr²h = \(\frac{4}{3}\)πR³ π × r² × (\(\frac{4r}{3}\)) = \(\frac{4}{3}\)π(4)³ (r)³ = (4)³ or r = 4 Therefore, radius of the base of the cylinder is 4 cm.

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.

Answer»

Radius of a sphere (R)= 4 cm

Height of the cylinder = \(\frac{2}{3}\) diameter

We know,

Diameter = 2(Radius)

Let h be the height and r be the base radius of a cylinder, then

h = \(\frac{2}{3}\) x (2r)

= \(\frac{4r}{3}\)

Volume of the cylinder = Volume of the sphere

πr²h = \(\frac{4}{3}\)πR³

π × r² × (\(\frac{4r}{3}\)) = \(\frac{4}{3}\)π(4)³

(r)³ = (4)³

or r = 4

Therefore, radius of the base of the cylinder is 4 cm.