Finding Area with Given Radius

A circular pool has a radius of 5 meters. What is its area?

Write the formula: $A = \pi r^2$ = Formula identified

Substitute the radius: $A = \pi \times 5^2$ = $A = \pi \times 25$

Multiply by π: $A = 25\pi$ or $A \approx 25 \times 3.14$ = $A \approx 78.5$

Add units: Area is measured in square units = $A \approx 78.5 \text{ m}^2$

Answer: The pool has an area of approximately 78.5 square meters (or exactly $25\pi$ m²).

Finding Area from Diameter

A circular table has a diameter of 120 cm. What is its area?

Find the radius: $r = \frac{d}{2} = \frac{120}{2}$ = $r = 60$ cm

Write the formula: $A = \pi r^2$ = Formula ready

Substitute and calculate: $A = \pi \times 60^2 = \pi \times 3600$ = $A = 3600\pi$

Approximate: $A \approx 3600 \times 3.14$ = $A \approx 11{,}304 \text{ cm}^2$

Answer: The table has an area of approximately 11,304 cm² (or about 1.13 m²).

Comparing Two Circles

Pizza A has radius 15 cm. Pizza B has radius 20 cm. How much more area does Pizza B have?

Calculate area of Pizza A: $A_A = \pi \times 15^2 = 225\pi$ = $A_A \approx 706.5 \text{ cm}^2$

Calculate area of Pizza B: $A_B = \pi \times 20^2 = 400\pi$ = $A_B \approx 1{,}256 \text{ cm}^2$

Find the difference: $A_B - A_A = 400\pi - 225\pi = 175\pi$ = Difference $\approx 549.5 \text{ cm}^2$

Find percentage increase: $\frac{175\pi}{225\pi} \times 100\%$ = About 78% more area

Answer: Pizza B has approximately 549.5 cm² more area—about 78% more pizza!

Mistake: Using diameter instead of radius in the formula

Why: The formula requires radius, not diameter. Using diameter gives an answer 4 times too large!

Correct: Always check: radius = diameter ÷ 2. Then use $A = \pi r^2$.

Mistake: Forgetting to square the radius

Why: Writing $A = \pi r$ instead of $A = \pi r^2$ gives a linear, not squared, relationship.

Correct: Remember: square the radius FIRST, then multiply by π. $A = \pi \times r \times r$

Mistake: Confusing area with circumference

Why: Circumference ($C = 2\pi r$) measures the perimeter. Area ($A = \pi r^2$) measures the space inside.

Correct: Area uses $r^2$ (squared), circumference uses $r$ (not squared).

Pizza Pricing

Understanding why a larger pizza is often better value per square centimeter.

A 30 cm diameter pizza for 12 euros vs two 20 cm pizzas for 8 euros each. Which is better value?

Garden Planning

Calculating mulch or soil needed for circular flower beds.

A circular flower bed has radius 2 meters. At 5 euros per square meter for mulch, the total cost is $\pi \times 4 \times 5 \approx 62.80$ euros.

Q: Why do we use π in the formula?

A: π (pi) is the ratio of a circle's circumference to its diameter. It appears in all circle calculations because circles have a unique curved shape. π ≈ 3.14159...

Q: What if I only know the diameter?

A: Divide the diameter by 2 to get the radius, then use the formula. Or use $A = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4}$.

Q: Should I use 3.14 or the π button on my calculator?

A: For exact answers, leave your answer in terms of π (like $25\pi$). For approximate answers, use your calculator's π button for precision, or 3.14 for quick estimates.