Student Concept Worksheet: Circumference & Area of Circles

The Big Idea

Every circle has the same special relationship between its measurements. The distance around any circle (circumference) is always about 3.14 times its diameter. The space inside (area) depends on the radius squared. These relationships are captured in formulas that use the special number pi (approximately 3.14).

Key Vocabulary

Radius (r)
Distance from center to edge (halfway across)

Diameter (d)
Distance across through center (d = 2r)

Circumference (C)
Distance AROUND the circle (perimeter)

Pi (approximately 3.14159...)
A special number that never ends!

Circumference Formulas

Circumference is the distance AROUND the circle - like a fence around a circular garden.

C = pi x d or C = 2 x pi x r

Both formulas work! Use whichever matches what you're given.

Example 1: Find the circumference of a circle with radius 7 cm.

Step 1: Identify what you're given: r = 7 cm

Step 2: Choose the formula with radius: C = 2 x pi x r

Step 3: Substitute: C = 2 x pi x 7 = 14 x pi

Step 4: Calculate: C = 14pi cm OR C = 14 x 3.14 = 43.96 cm

Example 2: Find the circumference of a circle with diameter 10 in.

Step 1: Identify what you're given: d = 10 in

Step 2: Choose the formula with diameter: C = pi x d

Step 3: Substitute: C = pi x 10 = 10pi

Step 4: Calculate: C = 10pi in OR C = 10 x 3.14 = 31.4 in

Area Formula

Area is the space INSIDE the circle - like the grass in a circular garden.

A = pi x r squared

MUST use radius! If given diameter, divide by 2 first!

Remember: r squared means r x r. Square the radius FIRST, then multiply by pi!

Example 3: Find the area of a circle with radius 5 m.

Step 1: Identify what you're given: r = 5 m

Step 2: Write the formula: A = pi x r squared

Step 3: Square the radius first: 5 squared = 5 x 5 = 25

Step 4: Multiply: A = pi x 25 = 25pi sq m OR A = 25 x 3.14 = 78.5 sq m

Example 4: Find the area of a circle with diameter 12 ft.

Step 1: Find the radius: r = d / 2 = 12 / 2 = 6 ft

Step 2: Write the formula: A = pi x r squared

Step 3: Square the radius: 6 squared = 6 x 6 = 36

Step 4: Multiply: A = pi x 36 = 36pi sq ft OR A = 36 x 3.14 = 113.04 sq ft

Guided Practice - Try These!

1 Find the circumference of a circle with radius 8 cm.

Exact answer: C = Approximate: C =

2 Find the circumference of a circle with diameter 14 inches.

Exact answer: C = Approximate: C =

3 Find the area of a circle with radius 6 m.

Exact answer: A = Approximate: A =

4 Find the area of a circle with diameter 20 ft.

Hint: First find the radius!

Exact answer: A = Approximate: A =

5 Word Problem: A circular swimming pool has a diameter of 18 feet. How much fencing is needed to go around the pool?

Answer:

6 Word Problem: A circular garden has a radius of 4 meters. How much area does the garden cover?

Answer: