Question

In the diagram, there are 14 cubes glued together to form a solid. Each cube has a volume of 1/8in^3. Find the surface area of the solid. (Show work)

Answer 1

`10(1)/(2)in^(2)`

Explanation:

If we solve for the surface area for each of the 14 cubes, we will come up with a surface area larger than the shape. The best way to go around this is to solve for each face of the shape.

The shape has a total of 42 faces.

The volume of a cube is s³, each cube is
`(1)/(8)in^(3)`or can be converted to
`((1)/(2)in)^(3)`. So a single cube have edges that are
`(1)/(2)in`.

The area of a single face of each cube is
`((1)/(2)in)^(2)`. We can also write this as
`(1)/(4)in^(2)`.

Now that we have the area of a single face in the shape, we simply multiply the area by 42 faces.

Surface Area =
`(1)/(4)in^(2)` x 42

Surface Area =
`10(1)/(2)in^(2)`