An 8 x 8 x 8 hollow cube is constructed from 1 x 1 x 1 cubes so that its six walls are 1 cube thick. The number of 1 x 1 x 1 cubes needed to make the hollow cube is
A.169
B.296
C.298
D.384
the inside space is a 6x6x6 cube. So, just subtract it: 8^3-6^3 = ?
To find the number of 1 x 1 x 1 cubes needed to make the hollow cube, we need to calculate the total volume of the hollow cube.
The outer dimensions of the hollow cube are 8 x 8 x 8, and the inner dimensions are (8 - 2) x (8 - 2) x (8 - 2), or 6 x 6 x 6.
The volume of the hollow cube can be calculated by subtracting the volume of the inner cube from the volume of the outer cube:
Volume of the outer cube = 8 x 8 x 8 = 512
Volume of the inner cube = 6 x 6 x 6 = 216
Volume of the hollow cube = Volume of the outer cube - Volume of the inner cube = 512 - 216 = 296
Therefore, the number of 1 x 1 x 1 cubes needed to make the hollow cube is 296.
Therefore, the answer is B. 296.
To find the number of 1x1x1 cubes needed to construct the hollow cube, we need to calculate the number of cubes on each face of the hollow cube.
We know that the dimensions of the hollow cube are 8 x 8 x 8, and the walls are 1 cube thick. This means that the inner area of the cube is 6 x 6 x 6.
To calculate the number of cubes on each face, we can use the formula for the volume of a rectangular prism: Volume = length x width x height. In this case, the length, width, and height of each face are 6, 6, and 1 respectively.
So the number of cubes on each face is 6 x 6 x 1 = 36.
Since there are 6 faces in total, the total number of cubes needed to make the hollow cube is 36 x 6 = 216.
However, we need to account for the 1x1x1 cubes that make up the corners and edges of the hollow cube. Each corner requires 1 cube, and each edge is made up of 2 cubes.
There are 8 corners, so we need to add 8 cubes for the corners.
There are 12 edges, and each edge requires 2 cubes. So we need to add 24 cubes for the edges.
Therefore, the total number of cubes needed to make the hollow cube is 216 + 8 + 24 = 248.
None of the given answer choices match the number we calculated (248 cubes), so none of the provided answers (A, B, C, D) are correct.