Question

When three equal cubes are joined end to end, the surface area of the resulting cuboid is 504 cm². Find the edge of each cube.

Answer 1

Let the edge of each cube be denoted as a cm.

When three equal cubes are joined end to end, the resulting shape is a cuboid with the following dimensions:

• Length of the cuboid = 3a (since there are three cubes joined end to end)
• Width of the cuboid = a (same as the edge of the cube)
• Height of the cuboid = a (same as the edge of the cube)

Step 1: Surface Area of the Cuboid

The formula for the surface area of a cuboid is:

Surface area = 2(lw + lh + wh)

where l, w and h are the length, width and height of the cuboid, respectively. 

Substitute the values for the length, width and height of the cuboid:

Surface area = 2((3a × a) + (3a × a) + (a × a))

Surface area = 2(3a² + 3a² + a²)

Surface area = 2 × (7a²) = 14a²

Step 2: Set the surface area equal to 504 cm²

We are given that the surface area of the resulting cuboid is 504 cm², so:

14a² = 504

Step 3: Solve for a

`a^2 = 504/14 = 36`

Take the square root of both sides:

`a = sqrt(36) = 6` cm