Area Breakdown
A rectangle has a semicircle cut out of it. How do you find the area of the remaining shape?
Find the area of the rectangle, then subtract the area of the semicircle.
If the diameter of a circle doubles, what happens to the area?
The area becomes 4 times larger
What is the formula for the area of a circle?
A = πr²
What do you measure if you need to know how much fencing is needed around a circular garden?
Circumference
A graph has "Diameter" on the x-axis. What might be on the y-axis if the relationship is proportional?
Circumference or radius
You have an L-shaped figure. How can you break it into simpler shapes to calculate the area?
Divide it into two rectangles, calculate their areas separately, and add them together
True or False: The area of a circle is proportional to its diameter.
False: The area of a circle is NOT proportional to its diameter.
What is the formula for the circumference of a circle?
C = 2πr or C = πd
What would the graph look like if it compared a circle’s radius to its area?
A square has a circle inscribed in it. What is the area of the shaded region outside the circle?
Find the area of the square and subtract the area of the circle.
Why is the relationship between diameter and area not proportional?
Graphically it is not proportional or there is no constant of proportionality between the two measurements.
A circle has a radius of 6 cm. What is its area? (Use π ≈ 3.14)
A = π(6²) = 3.14 × 36 = 113.04 cm²
A company is painting circular signs. Do they need to calculate circumference or area to determine the amount of paint needed?
Area
True or False: π is the constant of proportionality that relates the diameter of a circle to its circumference.
True
A garden is shaped like a composite figure made of a rectangle and a semicircle. How do you find the total area?
Find the area of the rectangle and the semicircle separately, then add them together.
Explain why doubling the radius does not double the area
Since A = πr², if r doubles (2r), then A = π(2r)² = 4πr², meaning the area is 4 times larger.
A circle’s circumference is 31.4 cm. What is its diameter? (Use π ≈ 3.14)
C = πd → 31.4 = 3.14d → d = 10 cm
A runner is jogging around a circular track. Should they use circumference or area to calculate how far they ran?
Circumference
Which is correct? A. π is the area of a circle with radius 1. B. π is the area of a circle with diameter 1.
π is the area of a circle with radius 1.
A playground has an irregular shape made of a square, a rectangle, and a quarter-circle. What steps would you take to determine the total area?
Break it into simpler shapes, calculate each area, and sum them up
A circle’s diameter is tripled. By what factor does the area increase?
9 times larger → A = π(3r)² = 9πr²
A circular pizza has a radius of 8 inches. If a new pizza has twice the diameter, how much larger is its area?
The new pizza has 4 times the area (since doubling the diameter quadruples the area).
Explain why two circles can have the same circumference but different areas.
If the circles are measured differently (e.g., outer vs. inner circles), their circumference may be the same, but their area depends on radius².
Which is correct? A. π is the circumference of a circle with radius 1. B. π is the circumference of a circle with diameter 1.
B. π is the circumference of a circle with diameter 1.