Volume of Prisms
This lesson introduces students to the concept of volume for prisms. It moves from simple cuboids to triangular prisms and cylinders, concluding with complex compound prisms and algebraic rearrangement of the volume formula.
Learning objectives
- Identify the constant cross-section of various prisms.
- Calculate the volume of prisms including cuboids and triangular prisms using a formula.
- Apply the volume formula to solve problems involving compound prisms and missing dimensions.
Lesson plan (60 minutes)
Starter · 10 min
Starter: Recall area of 2D shapes (rectangles, triangles, circles).
Introduction · 10 min
Teacher Explanation: Defining prisms and the universal formula V = Area of cross-section × length.
Guided Practice · 10 min
Guided Practice: Worked example on the board involving a triangular prism.
Independent Practice · 20 min
Independent Practice: Differentiated worksheets (Support, Core, Stretch).
Plenary · 10 min
Plenary: Multiple-choice quiz and self-marking.
Key vocabulary
- Prism
- A 3D solid with two identical ends and flat sides. The cross-section is the same all along its length.
- Cross-section
- The surface shape exposed by making a straight cut through a solid, usually at right angles to an axis.
- Volume
- The amount of 3D space an object occupies.
- Cylinder
- A prism with a circular cross-section.
- Cubic Centimetre (cm³)
- A unit of volume equal to a cube with sides of 1cm.
Core worksheet (first questions)
- Calculate the volume of a cube with side length 6cm. (Wait, a cuboid 6x5x6) - correction: Cuboid 6cm by 5cm by 6cm.
- A triangular prism has a right-angled triangle face with sides 3cm and 6cm. The prism is 5cm long. Find the volume.
- A triangular prism has a base of 7cm, a height of 3cm and a length of 10cm. Find the volume.
- Find the volume of a prism with a square cross-section (side 5cm) and length 10cm.
Quiz (sample)
1. What is the general formula for the volume of a prism?
- A. The perimeter multiplied by the height.
- B. The area of the cross-section multiplied by the length.
- C. The sum of all side lengths.
- D. Length times width times two.
2. What defines a prism?
- A. It is any 3D shape with straight edges.
- B. It has a constant cross-section throughout its length.
- C. It must have a triangular face.
- D. It is a shape where all sides are equal.
3. A prism has a cross-sectional area of 10 cm² and a length of 4 cm. What is its volume?
- A. 20 cm³
- B. 14 cm³
- C. 40 cm³
- D. 80 cm³
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