Lesson 3: Circle. Volume of a Cylinder. Scientific Notation
Lesson 3: Circle. Volume of a Cylinder. Scientific Notation
Circumference and area of a circle, volume of a cylinder, and scientific notation.
In this lesson you will learn about scientific notation and its significance when working with very large and very small numbers.
Scientific notation is widely used in Physics, Astronomy and Chemistry. For example, it could be used to express the volume of water in a large lake. Instead of writing all the zeros we multiply the number by a certain power of 10.
You will also learn how to calculate area and circumference of a circle.
You will discover the importance of the Pi number.
Here are the first 100,000 digits of Pi
The lesson teaches you how to determine the volume of a cylinder (a 3D shape with circular bases and a rectangular lateral part). You will also learn what calculating the volume means and what units should be used.
Sketching in 3D
Key ideas: Circle. Volume of a Cylinder. Scientific Notation
- Circumference C = πd = 2πr (π ≈ 3.14)
- Area of a circle A = πr2
- Volume of a cylinder V = (area of base) × height = πr2h
- Scientific notation writes a number as a × 10n, where 1 ≤ a < 10. Large numbers have a positive n; small numbers have a negative n.
Worked examples
Example 1
A circle has a radius of 5 cm. Find its circumference and area.
- C = 2π(5) = 10π ≈ 31.4 cm
- A = π(52) = 25π ≈ 78.5 cm2
Example 2
A can has a radius of 3 cm and a height of 10 cm. Find its volume.
- V = π(32)(10) = 90π ≈ 282.7 cm3
Example 3
Write in scientific notation: a) 45 000 000 b) 0.000 32
- a) Move the decimal 7 places left: 4.5 × 107
- b) Move it 4 places right: 3.2 × 10−4
Example 4
Calculate (3 × 104)(2 × 103).
- 3 × 2 = 6 and 104 × 103 = 107.
- 6 × 107
Common mistakes
- Using the diameter instead of the radius in A = πr2.
- Squaring π·r instead of just r.
- Writing 45 × 106: the first number must be between 1 and 10.
Questions students ask
Why do scientists use scientific notation?
It makes very large and very small numbers (like distances in space or sizes of cells) shorter to write and easier to compare.
Check your understanding
Practise with the Grade 8 quizzes. You’ll see right away if each answer is correct.