Question

Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose diagonal is 12 SQRT3 cm. Find the edges of the three cubes

Answer 1

Let edges of 3 cubes be 3x xm, 4x cm and 5x cm

So, voulme of single big cube = [(3x)3 + (4x)3 + (5x)3 ]cm3
Again, $\sqrt{ 27x3 + 64x3 + 125x3} = 12 \sqrt{3}$
or, 216x3 = 432
or, x = $\frac{x}{ \sqrt[3]{2} }$

So, edges of 3 cubes are 3$\frac{x}{ \sqrt[3]{2} }$ cm, 4 $\frac{x}{ \sqrt[3]{2} }$cm and 5$\frac{x}{ \sqrt[3]{2} }$ cm.