MathIsimple
Back to Unit 4

Lesson 4-3: Area & Circumference of Circles

Scenario: Garden Design - Design circular gardens and calculate materials needed!

Duration: 60-75 minutesScenario: Garden Design

Learning Objectives

  • Calculate area of circles using A = πr²
  • Calculate circumference using C = 2πr or C = πd
  • Understand the relationship between radius, diameter, and π
  • Apply circle calculations to real-world design problems

Garden Design Problem

Circular Flower Bed

You're designing a circular flower bed with a radius of 6 meters. You need to calculate the area for planting and the circumference for the border.

Questions:
1. How much area do you have for planting? (Area)
2. How much border material do you need? (Circumference)

r = 6 m

Visual representation of the circular flower bed

Step-by-Step Solution

Step 1: Calculate the area (planting space)

Area = π × r²
Area = π × 6²
Area = π × 36
Area = 3.14 × 36 = 113.04 m²

Step 2: Calculate the circumference (border material)

Circumference = 2 × π × r
Circumference = 2 × π × 6
Circumference = 12 × π
Circumference = 12 × 3.14 = 37.68 m

Answer: You have 113.04 m² for planting and need 37.68 m of border material.

Circle Formulas

Area Formula

A = π × r²

Area = π × radius²
Units: square units (m², ft², etc.)

Remember: π ≈ 3.14 (or use π button on calculator)

Circumference Formula

C = 2πr or C = πd

Circumference = 2 × π × radius
or Circumference = π × diameter
Units: linear units (m, ft, etc.)

Remember: diameter = 2 × radius

Understanding π (Pi)

What is π?

π (pi) is a special number that represents the ratio of a circle's circumference to its diameter. No matter how big or small the circle, this ratio is always the same!

π = circumference ÷ diameter ≈ 3.14159...

π is approximately 3.14 (or 22/7 for easier calculations)

3.14

Common approximation

22/7

Fraction approximation

π

Exact value (use calculator)

Practice Problems

Problem 1

A circular swimming pool has a diameter of 10 meters. Calculate the area and circumference of the pool.

Your solution:

Problem 2

A circular pizza has a radius of 8 inches. Find the area of the pizza and the length of crust around the edge.

Your solution: