Question

a cylinder whose height is two "-third" of its diameter ,has the same volume as a sphere of diameter 8 cm .find radius of the base of the cylinder

Answer 1

Answer:

Radius of the base of the cylinder is 4cm.

Step-by-step explanation:

According to the question, it is given that :

height= 2÷3 of its diameter..(i)

If radius is r,then

Diameter=2r

eq(i)..becomes

h=(2×2r)÷3

h=4r÷3

Now, it is given that:

Volume of the cylinder = volume of sphere of radius 4cm

Sphere has diameter=8cm

so, radius= 4cm

Hence, πr²h= (4πr³)÷3

r²h= 4(4)³÷3

Put h= 4r÷3

(r²×4r)÷3= (4×64)÷3

r³=64

r=∛64

r= 4cm

Hence, we get the radius ie.,4cm.