A solid metal cuboid has a volume of 600 cm3
.
(a) The base of the cuboid is 10 cm by 12 cm.
Calculate the height of the cuboid

### Solution:
The **volume** \( V \) of a cuboid is given by:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

In this problem:  
- **Volume** \( V = 600 \, \text{cm}^3 \)  
- **Base dimensions**: Length \( = 10 \, \text{cm} \) and Width \( = 12 \, \text{cm} \)  
- **Height** \( h \) is unknown.

#### Step 1: Write the volume equation
\[
600 = 10 \times 12 \times h
\]

#### Step 2: Simplify the equation
\[
600 = 120 \times h
\]

#### Step 3: Solve for height \( h \)
\[
h = \frac{600}{120} = 5 \, \text{cm}
\]

### Final Answer:
The height of the cuboid is \( 5 \, \text{cm} \).

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Do you want further details or have any other questions?  

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### 5 Related Questions:
1. How do you find the surface area of a cuboid?
2. If the material of the cuboid has a density of 8 g/cm³, what is its total mass?
3. What happens to the volume if the height is doubled?
4. How would you calculate the diagonal of this cuboid?
5. Can you find the height if only the surface area and volume are known?

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### Tip:
When working with volumes, always ensure that all dimensions are in consistent units to avoid calculation errors.

A solid metal cuboid has a volume of 600 cm³. The base of the cuboid is 10 cm by 12 cm. Calculate the height of the cuboid.

Learn how to calculate the height of a cuboid with a given volume of 600 cm³ and base dimensions of 10 cm by 12 cm. This step-by-step solution uses the formula for the volume of a cuboid, perfect for students in Grades 6-8.

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