Pizza Size Comparison

A small pizza has a diameter of 10 inches and costs 8 dollars. A large pizza has a diameter of 16 inches and costs 15 dollars. Which pizza gives you more pizza per dollar?

Find the radius of each pizza: Small: $r = 10 \div 2 = 5$ inches Large: $r = 16 \div 2 = 8$ inches = $r_{small} = 5$, $r_{large} = 8$

Calculate each area: Small: $A = \pi \times 5^2 = 25\pi \approx 78.5$ sq in Large: $A = \pi \times 8^2 = 64\pi \approx 201.1$ sq in = Small ≈ 78.5 sq in, Large ≈ 201.1 sq in

Find area per dollar: Small: $78.5 \div 8 \approx 9.8$ sq in per dollar Large: $201.1 \div 15 \approx 13.4$ sq in per dollar = Small: 9.8, Large: 13.4 sq in/dollar

Compare and conclude: $13.4 > 9.8$, so large pizza is better value = Large pizza wins!

Answer: The large pizza gives you about 13.4 square inches per dollar, compared to only 9.8 for the small. The large pizza is the better deal!

Swimming Pool Cover

A circular swimming pool has a radius of 6 meters. A pool cover costs 12 euros per square meter. How much will it cost to buy a cover for the entire pool?

Identify the given information: Radius $r = 6$ m, Cost = €12 per sq m = Need to find total area, then multiply by cost

Calculate the pool area: $A = \pi r^2 = \pi \times 6^2 = 36\pi$ = $A = 36\pi \approx 113.1$ square meters

Calculate the total cost: Cost $= 113.1 \times 12$ = Cost ≈ €1,357.20

Round appropriately for money: Round to nearest euro or cent as appropriate = €1,357

Answer: The pool cover will cost approximately €1,357.

Finding Radius from Area

A circular garden has an area of 50 square meters. What is the radius of the garden?

Write the area formula: $A = \pi r^2$ = We need to solve for $r$

Substitute the known area: $50 = \pi r^2$ = Isolate $r^2$

Solve for $r^2$: $r^2 = \frac{50}{\pi} = \frac{50}{3.14} \approx 15.92$ = $r^2 \approx 15.92$

Take the square root: $r = \sqrt{15.92} \approx 3.99$ = $r \approx 4$ meters

Answer: The radius of the garden is approximately 4 meters.

Mistake: Using diameter instead of radius in the formula

Why: The formula $A = \pi r^2$ requires the radius. If given diameter, you must divide by 2 first.

Correct: If diameter = 10, then radius = 5. Area = $\pi \times 5^2 = 25\pi$, NOT $\pi \times 10^2 = 100\pi$

Mistake: Forgetting square units in the answer

Why: Area is always measured in square units because it represents a 2-dimensional space.

Correct: If radius is in meters, area is in square meters (m²). Never write just 'meters' for area!

Mistake: Confusing area with circumference

Why: Area ($A = \pi r^2$) tells you the space inside. Circumference ($C = 2\pi r$) tells you the distance around.

Correct: For a pool cover (filling the inside), use area. For fencing around a garden, use circumference.

Mistake: Doubling the area when diameter doubles

Why: When radius doubles, area quadruples (because $r$ is squared). A 20-inch pizza isn't twice as big as a 10-inch—it's 4 times bigger!

Correct: If radius goes from 5 to 10: Old area = $25\pi$, New area = $100\pi$. That's 4 times larger!

Pizza Pricing

Pizza shops price by diameter, but you eat the area. Understanding this helps you find the best deal.

A 12-inch pizza has area $\pi \times 6^2 = 36\pi \approx 113$ sq inches. A 16-inch pizza has area $\pi \times 8^2 = 64\pi \approx 201$ sq inches—almost twice as much!

Lawn Care and Gardening

Knowing circle area helps calculate how much seed, mulch, or fertilizer you need for circular garden beds or lawns.

A circular flower bed with radius 2 m needs mulch. Area = $\pi \times 2^2 = 4\pi \approx 12.6$ sq m. If one bag covers 3 sq m, you need 5 bags.

Sports and Recreation

Many sports involve circular areas—wrestling mats, discus circles, center circles in soccer.

A wrestling mat has diameter 9 meters. Area = $\pi \times 4.5^2 = 20.25\pi \approx 63.6$ square meters.

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

A: Use the π button for more accuracy when possible. If told to use 3.14, that's fine for estimation. Some problems may ask you to leave your answer in terms of π (like $36\pi$ square inches).

Q: How do I know if a problem needs area or circumference?

A: Ask: Am I filling/covering the inside (area) or going around the edge (circumference)? Pool cover = area. Fence around a garden = circumference.

Q: Why is a large pizza so much bigger than it looks?

A: Because area grows with the square of the radius! A 16-inch pizza isn't 60% bigger than a 10-inch—it's actually 156% bigger (over 2.5 times the area)!