Problema Solution
The mass of a steel sphere varies directly as the cube of it's radius.
If the mass of a steel sphere of radius 2cm is 500g, find:
(i) the mass, in grams, of a sphere with 3cm radius
(ii) the radius, in cm, of a sphere of mass 1000g
Answer provided by our tutors
(i) the mass, in grams, of a sphere with 3 cm radius
Let 'm' represent the mass in grams, of a sphere with 3 cm radius.
500 : 2^3 = m : 3^3
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click here to see the equation solved for m
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m = 1,687.5 g
The mass of a sphere with radius 3 cm is 1,687.5 g.
(ii) the radius, in cm, of a sphere of mass 1000 g
Let 'r' represent the radius of a sphere of mass 1000 g.
500 : 2^3 = 1000 : r^3
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click here to see the equation solved for r
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r = 2.52 cm
The radius of s sphere of mass 1000 g is 2.52 cm.