Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.


Given is, two solid spheres of same metal. Density of both spheres are same.

Mass (weight) of larger sphere, M = 5920 g


Mass (weight) of smaller sphere, m = 740 g


Diameter of smaller sphere = 5 cm


radius of smaller sphere, r = 5/2 = 2.5 cm


Volume of smaller sphere, v = 4/3 πr3



v = 1375/21 cm3


We know, density = mass/volume


density of smaller sphere = m/v


…(i)


And density of larger sphere = M/V


density of larger sphere = 5920/V g/cm …(ii)


By equations (i) & (ii), we get


Density of smaller sphere = Density of larger sphere




Volume of the larger sphere = 523.81 cm3


4/3 πR3 = 523.81 [, volume of larger sphere = 4/3 πR3, where R = radius of the larger sphere]



R3 = 125


R = (125)1/3


R = 5


Thus, radius of the larger sphere is 5 cm.


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