Volume of a Prism Textbook Exercise - Corbettmaths - Free Printable

To solve the problem of calculating the volume of each prism, we need to use the general formula for the volume of a prism:

\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]

The base area depends on the shape of the base (e.g., rectangle, triangle, etc.). Let's calculate the volume for each prism step by step.

---

Prism (a): Rectangular Prism

- Base Shape: Rectangle
- Dimensions: Length = 6 cm, Width = 4 cm, Height = 3 cm
- Base Area: \( \text{Length} \times \text{Width} = 6 \times 4 = 24 \, \text{cm}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 24 \times 3 = 72 \, \text{cm}^3 \)

\[
\boxed{72}
\]

---

Prism (b): Triangular Prism

- Base Shape: Triangle
- Base Dimensions: Base = 6 cm, Height = 5 cm
- Height of Prism: 20 cm
- Base Area: \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 6 \times 5 = 15 \, \text{cm}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 15 \times 20 = 300 \, \text{cm}^3 \)

\[
\boxed{300}
\]

---

Prism (c): Trapezoidal Prism

- Base Shape: Trapezoid
- Base Dimensions: Top = 4 m, Bottom = 7 m, Height = 5 m
- Height of Prism: Not explicitly given, but we assume it is the vertical height of the trapezoid.
- Base Area: \( \frac{1}{2} \times (\text{Top} + \text{Bottom}) \times \text{Height} = \frac{1}{2} \times (4 + 7) \times 5 = \frac{1}{2} \times 11 \times 5 = 27.5 \, \text{m}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 27.5 \times 5 = 137.5 \, \text{m}^3 \)

\[
\boxed{137.5}
\]

---

Prism (d): Rectangular Prism (Cube-like)

- Base Shape: Rectangle
- Dimensions: Length = 40 cm, Width = 1.1 m = 110 cm, Height = 2 m = 200 cm
- Base Area: \( \text{Length} \times \text{Width} = 40 \times 110 = 4400 \, \text{cm}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 4400 \times 200 = 880000 \, \text{cm}^3 \)

\[
\boxed{880000}
\]

---

Prism (e): Triangular Prism

- Base Shape: Triangle
- Base Dimensions: Base = 7 cm, Height = 8 cm
- Height of Prism: 5.5 cm
- Base Area: \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 7 \times 8 = 28 \, \text{cm}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 28 \times 5.5 = 154 \, \text{cm}^3 \)

\[
\boxed{154}
\]

---

Prism (f): Trapezoidal Prism

- Base Shape: Trapezoid
- Base Dimensions: Top = 6 cm, Bottom = 9 cm, Height = 6 cm
- Height of Prism: 12 cm
- Base Area: \( \frac{1}{2} \times (\text{Top} + \text{Bottom}) \times \text{Height} = \frac{1}{2} \times (6 + 9) \times 6 = \frac{1}{2} \times 15 \times 6 = 45 \, \text{cm}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 45 \times 12 = 540 \, \text{cm}^3 \)

\[
\boxed{540}
\]

---

Prism (g): Triangular Prism

- Base Shape: Right Triangle
- Base Dimensions: Base = 22 cm, Height = 12 cm
- Height of Prism: 13 cm
- Base Area: \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 22 \times 12 = 132 \, \text{cm}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 132 \times 13 = 1716 \, \text{cm}^3 \)

\[
\boxed{1716}
\]

---

Prism (h): Trapezoidal Prism

- Base Shape: Trapezoid
- Base Dimensions: Top = 10 cm, Bottom = 40 cm, Height = 8 cm
- Height of Prism: Not explicitly given, but we assume it is the vertical height of the trapezoid.
- Base Area: \( \frac{1}{2} \times (\text{Top} + \text{Bottom}) \times \text{Height} = \frac{1}{2} \times (10 + 40) \times 8 = \frac{1}{2} \times 50 \times 8 = 200 \, \text{cm}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 200 \times 8 = 1600 \, \text{cm}^3 \)

\[
\boxed{1600}
\]

---

Prism (i): Triangular Prism

- Base Shape: Triangle
- Base Dimensions: Base = 11 cm, Height = 9 cm
- Height of Prism: 15 cm
- Base Area: \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 11 \times 9 = 49.5 \, \text{cm}^2 \)
- Volume: \( \text{Base Area} \times \text{Height} = 49.5 \times 15 = 742.5 \, \text{cm}^3 \)

\[
\boxed{742.5}
\]

---

Final Answers:

\[
\boxed{72, 300, 137.5, 880000, 154, 540, 1716, 1600, 742.5}
\]