Question

Three cubes of metal, whose edges are 3, 4 and 5 cm respectively, are converted and formed in
single cube. Find the diagonal of this cube.​

Answer 1

Step-by-step explanation:

A1 = 3 CM

A2 = 4 CM

A3 = 5 CM

A4 = ?

This means VOLUME OF CUBE FORMED = VOLUME OF CUBE1 +VOLUME OF CUBE2 + VOLUME OF CUBE3

A4^3 = A1^3 + A2^3 + A3^3

A4^3 = (3)^3 + (4)^3 + (5)^3

A4^3 = 27 + 64 + 125

A4^3 = 216

$a4 = \sqrt[3]{216}$

A4 = 6 CM

THEREFORE, DIAGONAL OF CUBE 4 = √3A4^2

= √3(6) ^2

= √3(36)

= 6√3 CM

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