Question

cylinder of radius 12cm contains water to a depth of 20 cm when a spherical iron bar is dropped to the cylinder and does the level of water is raised by 6.75cm find the radius of the ball

Answer 1

radius = R = 12cm

depth = height = H = 20cm

volume = V = ?

V = πR²H

V = 3.14×(12)²×20

V = 3.14×144×20

V = 63360

V = 9043.4cm³
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when we dropped the spherical ball on the cylinder then total volume

total volume of cylinder = volume of sphere + volume of cylinder

6.75+9043.4 = volume of sphere + 9043.2

9049.95-9043.2 = volume of sphere

6.75cm³ = volume of sphere

volume of sphere = 6.75cm³

4πr³/3 = 6.75cm³

4πr³ = 6.75cm³×3

4πr³ = 20.25cm³

4×3.14×r³ = 20.25cm³

12.56r³ = 20.25cm³

r³ = 20.25cm³/12.56

r³ = 1.612cm³

r = ³√1.612cm³

r = 1.051cm
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therefore radius of the sphere is 1.051cm