Count Painted Blocks in a Large Cube

Hi Ersan, let's solve this problem about a large cube made from smaller wooden blocks.

Stacie builds a cube using three hundred forty-three small blocks. We need to find how many of these blocks have at least one side painted green after the large cube is painted.

First, we need to find the dimensions of the large cube. Since it is a cube made of n cubed blocks, we take the cube root of three hundred forty-three.

Because seven times seven is forty-nine, and forty-nine times seven is three hundred forty-three, we know the side length is seven.

This means the large cube consists of seven blocks along each edge.

A common way to find the number of painted blocks is to subtract the unpainted blocks from the total number of blocks.

The unpainted blocks are the ones completely inside the cube, forming a smaller inner cube.