A cubical metal box of side 10 cm. is melted and reshaped into cuboidal box of dimensions in the retio 2:3:5 find dimensions of Cuboid.
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Answer:
Dimensions of cuboidal box = 6.42 cm , 9.63 cm and 16.05 cm
Explanation:
Cubical Box
a = 10cm
Volume = a^3 = 10^3 = 1000 cubic cm
Cuboidal Box
Let x be the constant for ratio
Dimensions = 2x*3x*5x
Volume = lbh = 2x*3x*5x = 30x^3 cubic cm
Since the cubical box is reshaped into cuboidal box -
Volume of cubical box = Volume of Cuboidal Box
1000 = 30x^3
1000/30 = x^3
100/3 = x^3
33.33 = x^3
(3.21)^3 = x^3
Since Powers are same equating the bases -
x = 3.21 cm
Dimensions of cuboidal box = 2*3.21 = 6.42 cm
= 3*3.21 = 9.63 cm
= 5*3.21 = 16.05 cm
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