Question

Question 1
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

Answer 1

True.

Let the radius of the sphere and cylinder be r.

Given, height of the cylinder = diameter of the base
$\Rightarrow h=2r$

Radius of sphere = Radius of cyllinder = r

According to the given condition,

Volume of sphere
$=\frac{2}{3}\times Volumeofcylinder$

$\Rightarrow \frac{4}{3}\pi r^3=\frac{2}{3}\times \pi r^2\times 2r$

$\Rightarrow \frac{4}{3}\pi r^3=\frac{4}{3}\pi r^3$

Hence, volume of the sphere is equal to two-third of the volume of a cylinder