Question

find the volume of a sphere is equal to the 2/3rd of the volume of a cylinder whose height and diameter are equal tot the diameter of the sphere.

Answer 1

Let radius of sphere = r​
Diameter of sphere = 2r

It is given that,
Diameter of cylinder = Diameter of sphere = 2r
So, radius of cylinder = r

Also,
Height of cylinder = Diameter of sphere = 2r

$$\begin{gathered} Volumeofcylinder=\pi r^{2}h=\pi r^2\left(2r\right)=2\pi r^3...\left(1\right) \\ Volumeofsphere=\frac{4}{3}\pi r^3=\frac{2}{3}\left(2\pi r^3\right)=\frac{2}{3}(Volumeofcylinder)(from(1\left)\right) \end{gathered}$$