The cubes if edges 6,8,1 cms are melted without loss of metal into a single cube.the edge of the new cuble will be 

To determine the edge length of the new cube formed by melting three cubes with edges 6 cm, 8 cm, and 1 cm, we start by calculating the volumes of the original cubes and then find the volume of the new cube.

1. Calculate the volumes of the original cubes:
   \[
   V_1 = 6^3 = 216 \text{ cm}^3
   \]
   \[
   V_2 = 8^3 = 512 \text{ cm}^3
   \]
   \[
   V_3 = 1^3 = 1 \text{ cm}^3
   \]

2. Sum the volumes to get the total volume:
   \[
   V_{\text{total}} = V_1 + V_2 + V_3 = 216 + 512 + 1 = 729 \text{ cm}^3
   \]

3. To find the edge length of the new cube, we take the cube root of the total volume:
   \[
   a = \sqrt[3]{729}
   \]

4. Since \(729\) is a perfect cube:
   \[
   a = 9 \text{ cm}
   \]

Therefore, the edge length of the new cube is 9 cm.

Would you like more details or have any questions about the solution? Here are some related questions:

1. What is the volume of a cube with an edge length of 10 cm?
2. How do you calculate the surface area of a cube with an edge length of 5 cm?
3. If you melt a cube of edge 3 cm and a cube of edge 4 cm, what will be the edge length of the resulting cube?
4. How do you find the diagonal of a cube with edge length 7 cm?
5. What is the formula for the volume of a cube?
6. If you double the edge length of a cube, by what factor does the volume increase?
7. What is the difference between the volume of a cube with edge length 6 cm and a cube with edge length 7 cm?
8. How do changes in edge length affect the volume of a cube?

**Tip:** When dealing with geometric shapes, knowing how to manipulate their basic properties like edge length, volume, and surface area can greatly simplify solving related problems.

Learn how to calculate the edge length of a new cube formed by melting cubes with edges 6 cm, 8 cm, and 1 cm. This problem involves finding the volume of each cube, summing them, and then calculating the cube root to find the edge length. Suitable for Grades 7-9 students learning geometry and volume calculations.

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