A solid cube with an edge 10 cm is melted to from two equal cubes. Find the ratio of the edge of the smaller cube to the edge of the bigger cube ?
volume of smaller cube=500cm^2
edge length= cubroot500
ratio of smaller to larger: cubroot(500/1000)= cubrt(1/2)
8,000
To find the ratio of the edge of the smaller cube to the edge of the bigger cube, we need to determine the size of each cube.
Given that the edge of the original cube is 10 cm, we need to find the length of the edge of each smaller cube after the melting process.
When a solid cube is melted and reformed into smaller cubes, the volume of the original cube remains the same.
The volume of a cube is calculated by raising the length of one of its sides to the power of 3. Therefore, the volume of the original cube is (10 cm)^3 = 1000 cm^3.
Since the original cube is divided into two equal smaller cubes, the volume of each smaller cube will be 1000 cm^3 divided by 2, which is 500 cm^3.
To find the edge length of each smaller cube, we need to find the cube root of 500 cm^3.
∛(500 cm^3) ≈ 7.937 cm (rounded to three decimal places).
Now we have the edge length of the smaller cube, which is 7.937 cm, and the edge length of the original (bigger) cube, which is 10 cm.
To find the ratio between the two, divide the edge length of the smaller cube by the edge length of the bigger cube:
7.937 cm ÷ 10 cm ≈ 0.794.
Therefore, the ratio of the edge length of the smaller cube to the edge length of the bigger cube is approximately 0.794.