The volume of a cuboid is 210 cm³. Its length is 7 cm and width is 6 cm. Determine theheight of the cuboid.

1. Break Down the Problem

To find the height of the cuboid, we will use the formula for the volume of a cuboid: $V = \text{length} \times \text{width} \times \text{height}$ Given:

• Volume $V = 210 \, \text{cm}^3$
• Length $= 7 \, \text{cm}$
• Width $= 6 \, \text{cm}$

2. Relevant Concepts

We need to rearrange the volume formula to solve for height. The formula can be rewritten as: $\text{height} = \frac{V}{\text{length} \times \text{width}}$

3. Analysis and Detail

Substituting the known values into the equation: $\text{height} = \frac{210 \, \text{cm}^3}{7 \, \text{cm} \times 6 \, \text{cm}}$

Calculating the denominator: $7 \, \text{cm} \times 6 \, \text{cm} = 42 \, \text{cm}^2$

Now, substituting back into the height formula: $\text{height} = \frac{210 \, \text{cm}^3}{42 \, \text{cm}^2}$

Performing the division: $\text{height} = 5 \, \text{cm}$

4. Verify and Summarize

The calculations show that the height of the cuboid is consistent with the original volume provided. All operations were double-checked to ensure the accuracy of the division and multiplication.

Final Answer

The height of the cuboid is $5 \, \text{cm}$.