Surface Area & Volume • Topic 3 of 3

Introduction to Prisms and Problem Solving

What is a Prism? A prism is a three-dimensional solid with two parallel, identical polygonal bases connected by rectangular lateral faces. The shape is named after its base.

Types of Prisms:

Base ShapePrism NameExample
TriangleTriangular prismToblerone chocolate box
SquareSquare prism (cube if all edges equal)Dice
RectangleRectangular prism (cuboid)Shoebox
PentagonPentagonal prismPencil (some types)
HexagonHexagonal prismNut (some types)

Formulas for Prisms:

MeasurementGeneral Formula
Lateral Surface Area (LSA)Perimeter of base × Height
Total Surface Area (TSA)LSA + 2 × Area of base
VolumeArea of base × Height

Comparison: Cylinder and Prism

  • A cylinder is like a prism with circular bases
  • A cube is a prism with square bases
  • A cuboid is a prism with rectangular bases

Problem Solving Tips:

  • Identify the shape (cube, cuboid, cylinder, triangular prism, etc.)
  • Write down given dimensions and what needs to be found
  • Choose the correct formula
  • Substitute values carefully
  • Pay attention to units (convert if necessary)
  • Check if the answer is reasonable
Volume Formulas — 3D ShapesCuboidV = l × b × he.g. 4×3×2 = 24 cm³CubeV = a³e.g. 5³ = 125 cm³CylinderV = πr²he.g. π×4²×10ConeV = ⅓πr²h⅓ of cylinderSphereV=⁴⁄₃πr³Volume = amount of 3D space occupiedHemisphere = ½ × ⁴⁄₃πr³ = ⅔πr³Units: cm³, m³, litre (1L = 1000 cm³)Capacity: volume of liquid a container can hold
Solved Examples
1
Worked Example
A rectangular prism has length 10 cm, width 4 cm, and height 5 cm. Find its volume and total surface area.
Solution- This is a cuboid - Volume = \(l \times w \times h = 10 \times 4 \times 5 = 200\) cm³ - TSA = \(2(lw + wh + hl) = 2(10×4 + 4×5 + 5×10)\) - \(= 2(40 + 20 + 50) = 2 \times 110 = 220\) cm² - **Answer:** Volume = 200 cm³, TSA = 220 cm² *Example 2: A triangular prism has a triangular base with sides 3 cm, 4 cm, 5 cm (right triangle) and height 10 cm. Find its volume. (Area of right triangle = \(\frac{1}{2} \times 3 \times 4 = 6\) cm²) Solution: - Base area = \(\frac{1}{2} \times 3 \times 4 = 6\) cm² - Volume = Base area × height = \(6 \times 10 = 60\) cm³ - **Answer:** 60 cm³ *Example 3: A cuboid-shaped water tank is 1.5 m long, 1 m wide, and 0.8 m high. How many liters of water can it hold? (1 m³ = 1000 liters) Solution: - Volume = \(l \times b \times h = 1.5 \times 1 \times 0.8 = 1.2\) m³ - Liters = \(1.2 \times 1000 = 1200\) liters - **Answer:** 1200 liters

Key Points

  • A prism has two parallel identical bases and rectangular lateral faces
  • Volume of any prism = Area of base × Height
  • Lateral Surface Area = Perimeter of base × Height
  • Total Surface Area = Lateral SA + 2 × Area of base
  • Cylinders are like prisms with circular bases
  • Always check units and convert if needed (e.g., liters to m³)
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Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.A prism has the same ___ throughout its length.
Explanation: Uniform cross-section.
Q2.The volume of a prism is:
Explanation: Base area $\times$ length.
Q3.A triangular prism has a ___ cross-section.
Explanation: Triangular.
Q4.A cuboid is a ___ prism.
Explanation: Rectangular.
Practice more MCQs → 📝 Assignment · 35 marks