The Area of a circle with radius r is:

A = πr²

Remember that π ≈ 3.14

*Example:*

Area of a circle with radius 3 inches is A = πr² = π9 ≈ 3.14 × 9 = 28.26 in²

Check out the **ADVANCED** tab. The exercises will further your understanding and help with building a bigger mental picture. It builds links between numbers and algebra. It is important to try alternative calculations or approaches, to sketch the shapes, label the shapes with the given numbers, tracking changes to units of measure, visualizing to cross-link the concepts of area and numbers. We use the numbers from this boiler top example. If you spend 30 – 60 min working with the different ideas in the ADVANCED page, you`ll remember key formulas easier and you`ll learn new skills faster.

### A Short Review

A = r²π which is sometimes written as A = πr²

or

These formulas all produce the same result.

*Note *: π/4 ≈ 0.785398163 ….

### Worksheet: Level 1

### Worksheet: Level 1 Sample Questions

**Example:**

**Further example:**

If the radius of a circle = 7, how long is its diameter?

### Worksheet: Level 1 Answer Key

**Answer:**

### Download Worksheet: Level 1

### Worksheet: Level 2

### Worksheet: Level 2 Sample Questions

Calculate the area of the following circles. Answer in decimals.

**Example:**

Radius = 35 cm, Area = ?

**Question:**

- r = 5, A = ?

**Further example:**

Calculate the area of a circle with a diameter of 24 ¾ inches

### Worksheet: Level 2 Sample Answer Key

**Answer:**

r² ⋅ ? = A

radius² × ? = area of circle

5² × ? = **78.5398**

### Download Worksheet: Level 2

### Worksheet: Level 3

### Worksheet: Level 3 Sample Questions

Calculate the area of the following circles. Answer in decimals.

Remember:

r² ⋅ ? = A

or

**Example:**

- What area does a circular patch of sheet metal have if the radius is 2400 mm?

**Further example:**

What`s the cross-sectional area of a water main line whose internal height is 1.8 m?

### Worksheet: Level 3 Sample Answer Key

**Answer:**

r² ⋅ ? = A

radius² × ? = area of circle

(2400 mm)² × ? = **18, 095, 573.68 mm²**

### Download Worksheet: Level 3

### Infosheet: Advanced

### Additional Information: One way To Get The Answer

**One way to get the answer**

Calculate the area of the top of a boiler (circle) if the diameter is 0.5 m

One way to get the answer, using the formula: A = r²π

Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look is like this:

Using a calculator, do the following:

Enter 0.25

Press x² button

Press x (multiplication) button (this could be omitted, depending on your calculator`s circuits)

Press **π** button or **2ndF** button then the **π** button, depending on how your calculator is laid out.

Press =

You should see **0.19634954** on your display.

### Additional Information: Another Way To Get The Answer

**Another way to get the answer**

Calculate the area of the top of a boiler (circle) if the diameter is 0.5 m

Another way to get the answer, using the formula

Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look is like this:

Using a calculator, do the following:

Enter **0.5**

Press **x²** button

Press **x** (multiplication) button (this could be omitted, depending on your calculator`s circuits)

Press **π** button or **2ndF** button then the **π** button, depending on how your calculator is laid out.

Press **÷** button

Enter **4**

Press **=**

You should see **0.19634954** on your display.

Get a $20-or-so dual-display scientific calculator, even if you can`t take it with you into the exam hall. A calculator is also a learning tool, Technology Use is one of the 9 Essential Skills you can`t do without.

### Additional Information: Advanced

**ADVANCED**

Compare the 2 circle area calculations. The results are the same, 0.1963 m^{2}. Both methods have exactly 3 calculations. The formulas are different.

The first method

A = r²π

has a division up front (d ÷ 2 = r), then a squaring (r²) and a multiplication by π. The order of multiplication is interchangeable, so the formula could also be written as A = πr². Try it.

The second method

Both of the fractions in the formulas for the second method can also be written as

So now we have 6 possible ways to calculate the area of circles. Same results, same number of steps, same amount of work.

A formula is a symbolic short-hand way to write the above 3-step procedures. Use a formula that`s easiest to remember for you.

- Memorizing numbers comes from an age when pocket calculators with π button were very expensive. Not anymore.
- In some trades, accuracy beyond 4 decimal digits is not required since laying out measurements for cutting and fitting is not practical beyond 1 or 2 decimal digits. Who has a microscope on the job to mark 5.28 mm or 3.579 inches? Any tenth of a mm or hundredth of an inch is impossible to see on a ruler or tape. In some trades, calculating with only a few decimal digits is fine.
- The trades that use diameter-based circle formulas to work with are the ones where cylindrical raw materials are described with diameter: piping trades, plumbing, boilermaking, machining, electrical trades, HVAC trades.

Trades where radius-based calculations dominate are the ones where drawing and laying out of circles and arches to build or to calculate cost of materials are frequent tasks: metal fabricating, sheet metal work, carpentry, tailoring, joinery, tile setting and flooring, bricklaying, stucco and lather work, architectural glazing, painting.

### Download Infosheet: Advanced