Three cubes with sides in the ratio of 3 : 4 : 5 are melted to form a single cube whose diagonal is 18√3 cm. The sides of the three cubes are:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 9 cm, 12 cm, and 15 cm.
Let the sides of the three cubes be 3x, 4x, and 5x
Then, volume of the new cube = [(3x)3 + (4x)3 + (5x)3] = 216x3
The diagonal of the cube = a√3
a√3 = 18√3
⇒ a = 18 (side of the big cube)
Now, According to the question,
⇒ 216x3 = 183
⇒ x3 = 27
⇒ x = 3
So, the sides of the three cubes = 3x, 4x, and 5x = 9, 12, and 15