Prisms & cylinders

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. 2Volume of a cylinderV = πr²h; halve a diameter first

   Methodr = 3, h = 10: 9π × 10 = 90π cm³

   Another way: π in at the end90π ≈ 90 × 3.14 = 282.6

3. 3Surface 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

4. 4Surface area of a cylinderCurved 2πrh; total 2πr² + 2πrh

   Methodr = 3, h = 10: 60π + 18π = 78π cm²

   Another way: Take out the factor2πr(r + h) = 6π × 13 = 78π

5. 5Prisms and cylinders at workRise = volume ÷ base area; 1 L = 1000 cm³

   Method600 ÷ 200 = 3 cm

   Another way: One cylinder minus anotherπR²h − πr²h = π(R² − r²)h

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 →

   The prism in the picture has a volume of 90 cm³, and its cross-section is a triangle 12 cm across and 3 cm high. How long is the prism?

   ▶Show the answer and working

   Answer: 5 cm

   The cross-section is 12 × 3 ÷ 2 = 18 cm², so the length = volume ÷ cross-section = 90 ÷ 18 = 5 cm.

2. Example 2Surface area of a prism →

   The prism in the picture has a trapezium as its cross-section, 9 cm along the top and 27 cm along the bottom, each slanting side 15 cm; it is 10 cm long. What is the area of all its sides together, in cm²?

   ▶Show the answer and working

   Answer: 660 cm²

   The sides open into one rectangle: the perimeter 9 + 27 + 15 + 15 = 66 cm, times the length 10: 660 cm².

3. Example 3Prisms and cylinders at work →

   How many cm³ is 30 L?

   • A. 30000 cm³
   • B. 3000 cm³
   • C. 30,000,000 cm³
   • D. 300 cm³

   Choose the right answer

   ▶Show the answer and working

   Answer: A. 30000 cm³

   1 L = 1000 cm³, so 30 L = 30 × 1000 = 30000 cm³.