Question

150 spherical marbles, each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

Answer 1

Diameter of spherical marbles = \(\frac{1.4}2\)cm 

= 0.7 cm 

Diameter of cylinder vessel \(\frac{7}2\) cm

= 3.5 cm 

Volume of 150 spherical balls =150 × \(\frac{4}3\)πR³

= \(\frac{{150}\times{4}\times{22}\times{0.7}\times{0.7}\times{0.7}}{{3}\times{7}}\) cm³

= 215.6 cm³ 

Let the rise in level of water be h cm 

Volume of rise in level of water (Volume of cylinder) = πr²h

= \(\frac{22}7\times3.5\times3.5\times{h}\)

Volume of Rise in level of water in the vessel = volume of 150 spherical balls 

⇒ (\(\frac{22}7\)) × 3.5 × 3.5 × h = 215.6 

⇒ h = \(\frac{{215.6}\times{7}}{{22}\times{3.5}\times{3.5}}\) cm

⇒ h = 5.6 cm