Question

The solid is made up of 3-cm cubes. All the surfaces of the solidare painted.(a) How many cubes have only two faces painted?(b) What is the surface area of the painted cubes?

Answer 1

Step by step explanation:

(a) How many cubes have only two faces painted?

As you can see in the diagram above, there are 4 on the front face, there will also be 4 on the back and another 4 missing that do not appear on those two faces (blue).

There are 12 cubes that have only 2 faces painted.

(b) What is the surface area of the painted cubes?

Each face of that cube has an edge of 9 cm, so the surface of each face must be:

`A_1=9cm\cdot9cm=81cm^2`

And since the cube has 6 faces, the total must be:

`\text{Area}=6\cdot81cm^2=486cm^2`

486 cm^2