Volume of Rectangular Prisms worksheet with labeled diagrams and dimensions for calculating volume.

To solve the problem of finding the volume of each rectangular prism, we use the formula for the volume of a rectangular prism:

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

Let's go through each part step by step.

---

Part (a)

- Dimensions: \( 9 \, \text{cm} \times 9 \, \text{cm} \times 9 \, \text{cm} \)
- Volume:
\[
\text{Volume} = 9 \, \text{cm} \times 9 \, \text{cm} \times 9 \, \text{cm} = 729 \, \text{cm}^3
\]

---

Part (b)

- Dimensions: \( 8 \, \text{in} \times 10 \, \text{in} \times 4 \, \text{in} \)
- Volume:
\[
\text{Volume} = 8 \, \text{in} \times 10 \, \text{in} \times 4 \, \text{in} = 320 \, \text{in}^3
\]

---

Part (c)

- Dimensions: \( 6 \, \text{yd} \times 5 \, \text{yd} \times 3 \, \text{yd} \)
- Volume:
\[
\text{Volume} = 6 \, \text{yd} \times 5 \, \text{yd} \times 3 \, \text{yd} = 90 \, \text{yd}^3
\]

---

Part (d)

- Dimensions: \( 8 \, \text{ft} \times 4 \, \text{ft} \times 6 \, \text{ft} \)
- Volume:
\[
\text{Volume} = 8 \, \text{ft} \times 4 \, \text{ft} \times 6 \, \text{ft} = 192 \, \text{ft}^3
\]

---

Part (e)

- Dimensions: \( 12 \, \text{mm} \times 10 \, \text{mm} \times 5 \, \text{mm} \)
- Volume:
\[
\text{Volume} = 12 \, \text{mm} \times 10 \, \text{mm} \times 5 \, \text{mm} = 600 \, \text{mm}^3
\]

---

Part (f)

- Dimensions: \( 4.5 \, \text{m} \times 1.5 \, \text{m} \times 2 \, \text{m} \)
- Volume:
\[
\text{Volume} = 4.5 \, \text{m} \times 1.5 \, \text{m} \times 2 \, \text{m} = 13.5 \, \text{m}^3
\]

---

Part (g)

- Dimensions: \( l = 9 \, \text{m}, w = 7 \, \text{m}, h = 3 \, \text{m} \)
- Volume:
\[
\text{Volume} = 9 \, \text{m} \times 7 \, \text{m} \times 3 \, \text{m} = 189 \, \text{m}^3
\]

---

Part (h)

- Dimensions: \( l = 12 \, \text{mi}, w = 2 \, \text{mi}, h = 3 \, \text{mi} \)
- Volume:
\[
\text{Volume} = 12 \, \text{mi} \times 2 \, \text{mi} \times 3 \, \text{mi} = 72 \, \text{mi}^3
\]

---

Part (i)

- Dimensions: \( l = 8 \, \text{km}, w = 4 \, \text{km}, h = 5 \, \text{km} \)
- Volume:
\[
\text{Volume} = 8 \, \text{km} \times 4 \, \text{km} \times 5 \, \text{km} = 160 \, \text{km}^3
\]

---

Part (j)

- Dimensions: \( l = 2 \, \text{in}, w = 6 \, \text{in}, h = 10 \, \text{in} \)
- Volume:
\[
\text{Volume} = 2 \, \text{in} \times 6 \, \text{in} \times 10 \, \text{in} = 120 \, \text{in}^3
\]

---

Part (k)

- Dimensions: \( l = 11 \, \text{mm}, w = 9 \, \text{mm}, h = 5 \, \text{mm} \)
- Volume:
\[
\text{Volume} = 11 \, \text{mm} \times 9 \, \text{mm} \times 5 \, \text{mm} = 495 \, \text{mm}^3
\]

---

Part (l)

- Dimensions: \( l = 5 \, \text{ft}, w = 7 \, \text{ft}, h = 7 \, \text{ft} \)
- Volume:
\[
\text{Volume} = 5 \, \text{ft} \times 7 \, \text{ft} \times 7 \, \text{ft} = 245 \, \text{ft}^3
\]

---

Final Answers

\[
\boxed{
\begin{array}{ll}
\text{(a)} & 729 \, \text{cm}^3 \\
\text{(b)} & 320 \, \text{in}^3 \\
\text{(c)} & 90 \, \text{yd}^3 \\
\text{(d)} & 192 \, \text{ft}^3 \\
\text{(e)} & 600 \, \text{mm}^3 \\
\text{(f)} & 13.5 \, \text{m}^3 \\
\text{(g)} & 189 \, \text{m}^3 \\
\text{(h)} & 72 \, \text{mi}^3 \\
\text{(i)} & 160 \, \text{km}^3 \\
\text{(j)} & 120 \, \text{in}^3 \\
\text{(k)} & 495 \, \text{mm}^3 \\
\text{(l)} & 245 \, \text{ft}^3 \\
\end{array}
}
\]