Question

A cylinder whose height is two-third of its diameter, has the same volume as that of a
sphere of radius 4 cm. Find the radius of base of the cylinder. CBSE2018-3M​

Answer 1

Answer:

4 cm

I hope that this will help you

Answer 2

☆☞QUESTION:-☜☆

A cylinder whose height is two-third of its diameter, has the same volume as that of a

sphere of radius 4 cm. Find the radius of base of the cylinder.

☆Concept:-☆

Taking out the variables of the question and equating it in the form of volumes.

☆ STEP BY STEP SOLUTION☆:-

Let the diameter of cylider be = x cm

And so its height will be 2/3 i.e,= 2/3 of x=2x/3.

Formula of:-

1) Volume of sphere= 4/3 πr³

2)Volume of cylinder=πr²h

as its diameter is "x cm".

thereby its radius will be x/2 cm ----> Cylinder.

So,moving forward and answering the question by equating the equations , here we go :)

☆The radius of sphere is given to be = 4cm.

=> 4/3 πr³=πr²h

=>4/3r³=r²h

=>4/3r=h-----(1)

radius of sphere =4 cm and height of cylinder= 2x/3 cm.

keeping this in equation one.

=>4/3 x 4=2x/3 cm

=>x=8cm (after solving).

=> but 'x' is the diameter her of cylinder,

so,radius= x/2 cm.

=> 8/2 cm.

=>4cm.

IS THE RADIUS OF CYLINDER.

ANSWER:-

4cm is the radius of cylinder.