150 spherical marbles, each of diameter 1.4 cm are dropped in a cylind

1.	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» 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

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»

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