https://file.aiquickdraw.com/mathbot/file/1739256577836crd8rpls.jpg

The image contains several rectangular prisms with their volumes and some missing dimensions. Let's go through them step-by-step and find the missing dimensions.

### Problem 3
- Volume = 231 in³
- Dimensions: Length = 3 in, Width = 7 in, Height = ?

To find the missing dimension (height), we use the formula for the volume of a rectangular prism:

\[
V = l \times w \times h
\]

Substitute the known values:

\[
231 = 3 \times 7 \times h
\]

Solve for \( h \):

\[
231 = 21h \implies h = \frac{231}{21} = 11 \, \text{in}
\]

So, the missing dimension is 11 in.

### Problem 4
- Volume = 6400 m³
- Dimensions: Length = 20 m, Width = 20 m, Height = ?

Using the same volume formula:

\[
V = l \times w \times h
\]

Substitute the known values:

\[
6400 = 20 \times 20 \times h
\]

Solve for \( h \):

\[
6400 = 400h \implies h = \frac{6400}{400} = 16 \, \text{m}
\]

So, the missing dimension is 16 m.

### Problem 5
- Volume = 18,000 cm³
- Dimensions: Length = ?, Width = 8 cm, Height = 30 cm

Using the formula:

\[
V = l \times w \times h
\]

Substitute the known values:

\[
18,000 = l \times 8 \times 30
\]

Solve for \( l \):

\[
18,000 = 240l \implies l = \frac{18,000}{240} = 75 \, \text{cm}
\]

So, the missing dimension is 75 cm.

### Problem 6
- Volume = 16 ft³
- Dimensions: Length = 8 ft, Width = 2 ft, Height = ?

Using the volume formula:

\[
V = l \times w \times h
\]

Substitute the known values:

\[
16 = 8 \times 2 \times h
\]

Solve for \( h \):

\[
16 = 16h \implies h = \frac{16}{16} = 1 \, \text{ft}
\]

So, the missing dimension is 1 ft.

---

Would you like more details or explanations on any of these steps? Let me know if you have any questions! Here's a list of related questions:

1. How do I calculate the volume of irregular shapes?
2. What happens to the volume if one of the dimensions is doubled?
3. How can the concept of volume be applied in real-life scenarios?
4. How do you convert volume units (e.g., from cubic inches to cubic centimeters)?
5. Can you find the volume of a cone using similar methods?

Tip: Always double-check the units for each dimension, as volume is very sensitive to the units used.

Find the missing dimension of the prism given its volume and other dimensions.

Learn how to find the missing dimension of a rectangular prism given its volume and other dimensions. This problem covers volume calculations, algebraic manipulation, and solving for unknowns. Suitable for students in Grades 6-8.

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