Question

343 identical pieces are put together to form a large cube. How many more such cubes will be required
cover this cube completely?​

Answer 1

Answer:

Answer=>150 cubes.

Step-by-step explanation:

As 343 small cubes put together to form large cube, each edge of large cube have ∛343 = 7 small cubes. Only the small cubes on middle of large cube surface will be one-face painted. On each face, one face-painted cubes are (7-2)×(7-2) = 25. Total number of cubes with one face painted is 25×6 = 150 cubes.

Hope this helps you.

Answer 2

Given: 343 identical pieces are put together to form a large cube.

To find: The number of more such cubes that will be required to cover this cube completely.

Solution:

The cube root of 343 is 7. This means that one row or one column of the cube consists of 7 cubes and one face of the cube consists of 49 cubes. In order to find the number of cubes to cover the large cube, the following calculations must be made.

A layer of cubes will be required on each face of the large cube. There are 49 cubes on one face and there are 6 faces.

$49 * 6 = 294$

To cover the cube completely cubes will be required on the edges and corners as well. There must be 7 cubes on each edge and there are 12 edges. There must be 1 cube on one corner and there are 8 corners.

$7 * 12 = 84$

$1 * 8 = 8$

So the total number of cubes are

$294 + 84 + 8 = 386$

Therefore, the number of more such cubes that will be required to cover this cube completely is 386.