Question
Download Solution PDFThree 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Three cubes with sides in the ratio of 3 ∶ 4 ∶ 5 are melted to form a single cube whose diagonal is 18√3 cm.
Concept used:
The diagonal of a cube = √3a (where a is the sides)
Calculation:
Let the s sides of the cubes will be 3x cm , 4x cm, and 5x cm
As per the question,
Volume of the new cube is
(3x)3 +( 4x)3 +( 5x)3 = 216 x3.
⇒ side is = 6x
diagonal is 6x√3
⇒ 6x√3 = 18√3
⇒ x = 3
The sides of the cubes will be 9 cm , 12 cm, and 15 cm
∴ The correct option is 2
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