Question
Download Solution PDFThree cubes of sides 5 cm, 4 cm and 3 cm are melted to form a new cube. Find the length of the diagonal of the new cube.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Side of cube1 = 5 cm
Side of cube2 = 4 cm
Side of cube3 = 3 cm
Concept:
Volume of a cube = Side³;
Diagonal of a cube = √3 × Side
Solution:
⇒ Volume of new cube = Volume of cube1 + Volume of cube2 + Volume of cube3
⇒ Volume of new cube = 53 + 43 + 33
⇒ Volume of new cube = 125 + 64 + 27
⇒ Volume of new cube = 216 cm³
⇒ Side of new cube = ∛Volume of new cube
⇒ Side of new cube = ∛216
⇒ Side of new cube = 6 cm
⇒ Diagonal = √3 × Side
⇒ Diagonal =
Therefore, the length of the diagonal of the new cube is
Last updated on Jul 8, 2025
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