To find the length of the cuboid, we use the volume formula for a cuboid:

$\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$

Given:

• Volume = 2415 mm³
• Height = 23 mm
• Width = 7 mm
• Length = ? (denoted as $L$)

Step-by-Step Solution:

1. Substitute the known values into the formula:

   $2415 = L \times 7 \times 23$

2. Calculate $7 \times 23$:

   $7 \times 23 = 161$

   So the equation simplifies to:

   $2415 = L \times 161$

3. Solve for $L$ by dividing both sides by 161:

   $L = \frac{2415}{161}$

4. Perform the division:

   $L = 15.0$

Final Answer:

$\mathbf{L = 15.0 \text{ mm}}$

Let me know if you need further clarifications!

Related Questions:

1. How do you calculate the volume of a cuboid when all three dimensions are known?
2. If the width were doubled, what would be the new volume?
3. What is the surface area of this cuboid?
4. How would the volume change if the height were halved?
5. What are the units used in volume calculations, and why?

Tip:

Always check your units when solving geometry problems to ensure consistency in measurements!