Question

3 cubes of sides are in the ratio of 3:4:5 are melted to form a new cube of diagonal 15√3.Find the measure of sides of initial cubes

Answer 1

Ratio of the sides: 3:4:5

Let the edges of the 3 cubes be:

3x, 4x and 5x

Vol of 3 small cubes  = Vol of big cube

(3x)³ + (4x)³ + (5x)³ = 216x³

Diagonal = ∛216x³

= 12√3

√a²+a²+a² = 12√3

a√3 = 12√3

a = 12

x = 12/6

x = 2

Sides of the initial cubes are:

3x = 6cm

4x = 8cm

5x = 10cm

Answer 2

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