Question

A solid cube with an edge 10 cm is melted to form two equal cubes.The ratio of the edge of the smaller cube to the edge of the bigger cube is

(a) \(\big(\frac13\big)^{\frac13}\)

(b) \(\frac12\)

(c) \(\big(\frac12\big)^{\frac13}\)

(d) \(\big(\frac14\big)^{\frac13}\)

Answer 1

(c) \(\bigg(\frac{1}{2}\bigg)^\frac13\)

Volume of the bigger cube = (10)³ cm³ = 1000 cm³ 

Volume of the smaller cube = 500 cm³ 

Required ratio = \(\frac{\text{Edge of smaller cube}}{\text{Edge of bigger cube}}\)

= \(\frac{(500)^{\frac13}}{(1000)^{\frac13}}\) = \(\bigg(\frac{(500)}{(1000)}\bigg)^\frac13\) = \(\bigg(\frac{1}{2}\bigg)^\frac13\)