This lesson is about calculating two important properties of 3D shapes: Surface Area (the total area covering the outside of the shape) and Volume (the space the shape occupies). We will focus on the right circular cylinder and the right triangular prism.

Part A: The Right Circular Cylinder

1. Core Concepts & Formulas

A cylinder is made of two identical circular bases and one curved side.

• r = radius of the circular base

• h = perpendicular height of the cylinder

Surface Area: To find this, we "unroll" the cylinder into its flat parts: two circles and one rectangle.

• Area of the two circles (top & bottom): 2 × πr²

• Area of the curved surface: This is a rectangle where the height is h and the length is the circumference of the circle (2πr).

  • Area of curved surface = 2πrh

• Total Surface Area (for a closed cylinder): A = 2πr² + 2πrh

Volume:

• The formula is (Area of the base) × height.

• Volume of a Cylinder (V): V = πr²h

2. Exam Tips for Cylinders

• Radius vs. Diameter TRAP: A very common exam trick is to give you the diameter. Your first step should always be to divide it by 2 to get the radius (r) before you use any formula.

• Read the Question Carefully - Is it Open or Closed?

  • An "open top" cylinder or a "tin without a lid" has only one circular base. Its surface area is A = πr² + 2πrh.

  • A "pipe" or "hollow cylinder" has no top or bottom. Its surface area is just the curved part: A = 2πrh.

• Working Backwards: If you are given the Volume and asked to find the height (h), rearrange the formula: h = V / (πr²).

Part B: The Right Triangular Prism

1. Core Concepts & Formulas

A triangular prism has 5 faces: two identical triangles (the bases or cross-sections) and three rectangles (the sides).

Surface Area: There's no single magic formula. You must find the area of all 5 faces individually and then add them together.

• Step 1: Find the area of one triangle (½ × base × height) and multiply by 2.

• Step 2: Find the area of each of the three rectangles (length × width).

• Step 3: Add all the areas from Step 1 and Step 2 together.

Volume:

• The formula is (Area of the cross-section) × length.

• Volume of a Triangular Prism (V): V = (Area of the triangular face) × (Length of the prism)

2. Exam Tips for Prisms

• Pythagoras' Theorem is often required! For surface area problems, if the triangular face is a right-angled triangle, you might only be given two of its side lengths. You will need to use Pythagoras' Theorem (a² + b² = c²) to find the third side before you can calculate the area of all the rectangular faces.

• Identify the Cross-Section: The cross-section is the triangular face. The "length" of the prism is the distance that connects the two triangular faces. Don't get confused if the prism is lying on its side.

• Be Systematic: When calculating surface area, list the area of each of the 5 faces separately before adding them up. This reduces errors.

  • Area of Triangle 1 = ...

  • Area of Triangle 2 = ...

  • Area of Rectangle (base) = ...

  • Area of Rectangle (side 1) = ...

  • Area of Rectangle (side 2) = ...

  • Total Surface Area = Sum of the above

3. Overall Important Points

• UNITS:

  • Surface Area is always in square units (e.g., cm², m²).

  • Volume is always in cubic units (e.g., cm³, m³).

• VOLUME CONVERSIONS: You must know these for capacity problems.

  • 1 litre = 1000 cm³

  • 1 m³ = 1000 litres

• Show Your Formulas and Steps: Always write down the main formula you are using before putting in the numbers. This is essential for getting method marks.