Question

if a sphere of radius r entered in side a cylinder tightly the volume of the cylinder is​

Answer 1

Answer:

Vol of cylinder = πr 2h

here h=2r

The formula becomes

πr 2x2r=2πr ^3

Answer 2

The volume of the cylinder is $2\pi r^3$

Step-by-step explanation:

Given:

The radius of the sphere is 'r'.

The sphere fits tightly inside the cylinder. The radius of the cylinder is thus equal to the radius of the sphere. Also, the diameter of the sphere must be equal to the height of the cylinder so that the sphere completely fits inside the cylinder.

Therefore, the radius of the cylinder is 'r'. The height of the cylinder is twice the radius and thus is equal to '2r'.

Now, volume of a cylinder is given as:

$V=\pi r^2 h\\V=\pi r^2 (2r)\\V=2\pi r^{2+1}\\ V=2\pi r^3$

Therefore, the volume of the cylinder is $2\pi r^3$.