Three cubes each of volume 125 cm are joined end to end to form a cuboid. find the total surface area of cuboid.
v=s^3 = 125
so s = 5
L = 3 s
area of sides = 4 (3 s * s) = 12 s^2
area of ends = 2 s^2
total = 14 s^2 = 14 * 25
Wouldn't you be just hiding 4 faces ?
Visualize it, or sketch the 3 dice joined.
LOL - good point
To find the total surface area of the cuboid formed by joining three cubes end to end, we need to break down the problem into smaller steps.
Step 1: Find the dimensions of the cuboid
Since each cube has a volume of 125 cm³, we know that the length, width, and height of each cube are equal, and therefore the side length of each cube is 5 cm (since 5^3 = 125).
When three of these cubes are joined end to end to form a cuboid, the length and width of the cuboid will remain the same, while the height will triple. So, the dimensions of the cuboid are 5 cm (length), 5 cm (width), and 15 cm (height).
Step 2: Calculate the surface area of the cuboid
The surface area of a cuboid can be found by adding the areas of its six faces. In this case, we have:
- Two faces with dimensions 5 cm x 5 cm (length x width) = 25 cm² each.
- Two faces with dimensions 5 cm x 15 cm (length x height) = 75 cm² each.
- Two faces with dimensions 15 cm x 5 cm (width x height) = 75 cm² each.
Therefore, the total surface area of the cuboid is:
2(25 cm²) + 2(75 cm²) + 2(75 cm²) = 50 cm² + 150 cm² + 150 cm² = 350 cm².
Therefore, the total surface area of the cuboid formed by joining three cubes each with a volume of 125 cm³ is 350 cm².