Prisms

Skills and methods in this topic, easy to hard

1. 1Volume of a prismVolume = cross-section area × length

   Method6 × 8 ÷ 2 = 24, 24 × 10 = 240 cm³

   Another way: Two make a cuboid6 × 8 × 10 ÷ 2 = 240

2. 2Surface area of a prism2 × cross-section area + perimeter × length

   Method2 × 6 + 12 × 10 = 132 cm²

   Another way: Face by face6 + 6 + 30 + 40 + 50 = 132

3. 3Prisms at work: capacity and water levelsRise = volume ÷ base area; 1 L = 1000 cm³

   Method600 ÷ 200 = 3 cm

   Another way: Volume in step with depthdepth × 2 → volume × 2

Worked examples

From different skills in this topic. Have a go first, then open each one for the answer and the working.

1. Example 1Volume of a prism →

   A prism has a base area of 36 cm², and its two ends are 22 cm apart. What is its volume, in cm³?

   ▶Show the answer and working

   Answer: 792 cm³

   A prism's volume = base area × height (the distance between its ends) = 36 × 22 = 792 cm³.

2. Example 2Surface area of a prism →

   The prism in the picture has a right-angled triangle with sides 15 cm, 8 cm and 17 cm as its cross-section, and is 11 cm long. What is its total surface area, in cm²?

   ▶Show the answer and working

   Answer: 560 cm²

   The two ends 2 × (15 × 8 ÷ 2) = 120, the sides = perimeter × length = 40 × 11 = 440; 560 cm² in all.

3. Example 3Prisms at work: capacity and water levels →

   A cuboid tank is 40 cm long, 10 cm wide and 60 cm high inside (1 L = 1000 cm³). At most how many litres of water does it hold?

   ▶Show the answer and working

   Answer: 24 L

   It holds 40 × 10 × 60 = 24000 cm³ = 24000 ÷ 1000 = 24 L.