Question

ii) A cylindrical vessel of diameter 6cm contains some water in it. A few solid spheres each of radius 1-5cm were completely immersed into the water of the cylindrical vessel. How many spheres are required to be immersed so that the level of water rises by 2m.​

Answer 1

Step-by-step explanation:

Given, diameter of speher = 6 cm

⇒ radius of sphere R=6/2 =3cm

Diameter of cylindrical vessel = 12 cm

⇒ radius of cylindrical vessel = r= 2/12 =6cm

volume of sphere = 34

πR 3 = 34

π2 (3) 2

Volume of cylindrical vessel = πr 2 h=π×6

2 ×h

Here, the volume of sphere = volume increased in the cylindrical vessel.

∴ 34

π(3)

3 =π(6) 2 h

h= 34

× 63

= 6×64×3×3

= 33 =1cm

∴ 1 cm level of water rise in the cylindrical vessel.