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)

Accepted Solution

Answer:[tex]10\dfrac{1}{2}in^{2}[/tex]Step-by-step 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 sΒ³, each cube is [tex]\dfrac{1}{8}in^{3}[/tex]or can be converted to [tex](\dfrac{1}{2}in)^{3}[/tex]. So a single cube have edges that are [tex]\dfrac{1}{2}in[/tex]. The area of a single face of each cube is [tex](\dfrac{1}{2}in)^{2}[/tex]. We can also write this as [tex]\dfrac{1}{4}in^{2}[/tex].Now that we have the area of a single face in the shape, we simply multiply the area by 42 faces.Surface Area = [tex]\dfrac{1}{4}in^{2}[/tex] x 42Surface Area = [tex]10\dfrac{1}{2}in^{2}[/tex]