The number of cubic blocks needed to fill the cube with side length 3/7 inch is 27.
To determine the number of cubic blocks needed to fill a cube, we can calculate the volume of the cube and the volume of a single cubic block, and then divide the volume of the cube by the volume of the block.
The volume of a cube is calculated by multiplying the length of one side by itself three times (since a cube has three equal sides). In this case, the side length of the cube is 3/7 inch, so its volume would be (3/7) x (3/7) x (3/7) cubic inches.
The volume of a single cubic block is calculated in a similar way. The side length of the block is 1/7 inch, so its volume would be (1/7) x (1/7) x (1/7) cubic inches.
Now, we can divide the volume of the cube by the volume of the block to find the number of blocks needed:
[(3/7) x (3/7) x (3/7) cubic inches] ÷ [(1/7) x (1/7) x (1/7) cubic inches]
Simplifying the expression:
(3/7) x (3/7) x (3/7) ÷ (1/7) x (1/7) x (1/7)
Canceling out the common factors:
3 x 3 x 3 ÷ 1 x 1 x 1
27 ÷ 1