A cylindrical vessel of diameter 4 cm is partlyfilled with water. If 3

1.	A cylindrical vessel of diameter 4 cm is partlyfilled with water. If 300 metallic balls aredropped in the cylinder then the rise in waterlevel is 0.8 cm, find the radius of each ball.a) 0.2 cme) 0.6 cmb) 0.4 cmd) 1 cmmade out of a
Answer» Diameter of the vessel = 4 cm Radius of the vessel = 2 cm Rise in water level = 0.8 cm Volume of the increased water level = πr²h = 22/7 × (2)²× 0.8 = 10.06 cu cm. Volume of 300 lead balls = 10.06 cu cm But, volume of 300 balls = 300 × 4/3 × 22/7 × (r)³ ⇒ 300 × 4/3 × 22/7 × (r)³= 10.06 ⇒ (r)³ = 10.06 × 1/300× 3/4× 7/22 ⇒ (r)³≅ 0.008 ⇒ r = 0.2 So, the radius of each ball is 0.2 cm

A cylindrical vessel of diameter 4 cm is partlyfilled with water. If 300 metallic balls aredropped in the cylinder then the rise in waterlevel is 0.8 cm, find the radius of each ball.a) 0.2 cme) 0.6 cmb) 0.4 cmd) 1 cmmade out of a

Answer»

Diameter of the vessel = 4 cm

Radius of the vessel = 2 cm

Rise in water level = 0.8 cm

Volume of the increased water level = πr²h

= 22/7 × (2)²× 0.8 = 10.06 cu cm.

Volume of 300 lead balls = 10.06 cu cm

But, volume of 300 balls = 300 × 4/3 × 22/7 × (r)³

⇒ 300 × 4/3 × 22/7 × (r)³= 10.06

⇒ (r)³ = 10.06 × 1/300× 3/4× 7/22

⇒ (r)³≅ 0.008

⇒ r = 0.2

So, the radius of each ball is 0.2 cm