Question

Три золотых куба с ребрами 3 см, 4 см,2 см переплавлены в один куб.какую длину имеет ребро этого куба?

Answer 1

Vкуба=a³
V₁=3³=27
V₂=4³=64
V₃=2³=8
V=V₁+V₂+V₃
V=27+64+8
V=99
a=∛99
ответ: ребро полученного куба ∛99

Answer 2

Calculating the Length of the Melted Cube's Edge

To calculate the length of the edge of the melted cube, we can use the formula for the volume of a cube, which is given by:

Volume = (Edge Length)^3

Given that three cubes with edge lengths of 3 cm, 4 cm, and 2 cm are melted into one cube, we can find the total volume of the melted cube by adding the volumes of the individual cubes.

The total volume of the melted cube is: Volume = (3 cm)^3 + (4 cm)^3 + (2 cm)^3

Let's calculate the total volume and then find the length of the edge of the melted cube.

Calculation

Using the given edge lengths: Volume = (3 cm)^3 + (4 cm)^3 + (2 cm)^3 Volume = 27 cm^3 + 64 cm^3 + 8 cm^3 Volume = 99 cm^3

To find the length of the edge of the melted cube, we can use the formula: Edge Length = (Volume)^(1/3)

Substituting the calculated volume: Edge Length = (99 cm^3)^(1/3) Edge Length ≈ 4.626 cm

Conclusion

The length of the edge of the melted cube is approximately 4.626 cm.