Question

A solid metal spherical ball of radius 7cm is put inside a cylinder of radius 5cm and height 13cm. if the cylinder is now filled completely with water, find the volume of the water inside the cylinder

Answer 1

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Given radius of the cylinder, r = 12 cm It is also given that a spherical iron ball is dropped into the cylinder and the water level raised by 6.75 cm Hence volume of water displaced = volume of the iron ball Height of the raised water level, h = 6.75 m Volume of water displaced = πr2h = π × 12 × 12 × 6.75 cm3 ⇒ Volume of iron ball = π × 12 × 12 × 6.75 cm3 → (1) But, volume of iron ball = From (1) and (2) we get ⇒ r3 = 33 ∴ r = 9 Thus the radius of the iron ball is 9 cm