Question

Three cubes with sides in the ratio 3 : 4 : 5 are melted to form a single cube whose diagonal is 12√3 cm. The sides of the cube are

(a) 6 cm, 8 cm, 10 cm 

(b) 3 cm, 4 cm, 5 cm 

(c) 9 cm, 12 cm, 15 cm 

(d) 12 cm,16 cm, 20 cm

Answer 1

(a) 6 cm, 8 cm, 10 cm

Let the sides of the three cubes be 3k, 4k and 5k respectively. 

∴ Volume of the new cube formed by melting the three cubes = (3k)³ + (4k)³ + (5k)³ 

= 27k³ + 64 k³ + 125k³ = 216k³ 

⇒ Each edge of the new cube = \(\sqrt{216k^3}\) = 6 k 

∴ Diagonal of the new cube = 6k√3  

Given, 6k√3 = 12√3 ⇒ 6k = 12 ⇒ k = 2 

∴ Sides of the three cubes are 6 cm, 8 cm and 10 cm respectively.