Circles: Circumference and Area

Mathematics · Geometry · ages 12-14

Name ______________________ Date ____________

A fan blade tip spins around in a circle with a radius of 10 cm. How far does the tip travel in one full spin? Use pi ≈ 3.14 and give your answer in centimeters.
Answer: ______________
A circle has a diameter of 10 cm. Which calculation finds its circumference?
- π × 10
- π × 10²
- 2 × 10
For any circle, the circumference is always about 3.14 times the diameter.
Circle one: True False
What does the number π describe in circle formulas?
- The ratio of circumference to diameter
- The ratio of area to radius
- The number of sides a circle has
A pizza shop offers to double the radius of your pizza for free. If the radius doubles, what happens to the amount of pizza?
- It stays the same
- It doubles
- It quadruples
- It triples
Is it possible for a circle's area and its circumference to have the same number value? Find the radius that makes this happen.
Answer: ______________
A wheel has a diameter of 0.5 m. How many full turns does the wheel need to roll 31.4 m? Use pi ≈ 3.14.
Answer: ______________
A house-shaped sign is made of a rectangle 6 cm wide and 8 cm tall, with a triangle roof on top. The triangle has a base of 6 cm and a height of 4 cm. What is the total area of the sign in square centimeters?
Answer: ______________
A running track is a rectangle 40 m long and 20 m wide, with a semicircle attached to each short end (each semicircle has a diameter of 20 m). Using π ≈ 3.14, what is the total distance around the track, to the nearest whole meter?
- 206 m
- 120 m
- 143 m
Zara wants the area of a circle with diameter 8 cm. She writes: A = π × 8² = 3.14 × 64 = 200.96 cm². What mistake did she make?
- She squared the wrong number of times
- She used the diameter instead of the radius in the formula
- She forgot to multiply by π

Answer key

For grown-ups. Fold this page away before handing over the rest.

Circles: Circumference and Area W1-mt_svFa6_mjO_-s1

62.8 · One full spin is one circumference: C = 2 x pi x r = 2 x 3.14 x 10 = 62.8 cm.
π × 10 · Circumference uses C = πd, so you multiply the diameter by π, not square it.
True · That constant ratio is π, and it is the same for every circle, big or small.
The ratio of circumference to diameter · π is the constant number you get when you divide any circle's circumference by its diameter, about 3.14.
It quadruples · Area grows with the square of the radius: pi x (2r)^2 = 4 x pi x r^2, so you get 4 times the pizza.
2 · Setting pi x r^2 equal to 2 x pi x r and solving gives r = 2 units.
20 · Each turn covers one circumference: C = pi x d = 3.14 x 0.5 = 1.57 m. Then 31.4 / 1.57 = 20 turns.
60 · Rectangle area is 48 cm^2 and triangle area is 12 cm^2, so the total is 60 cm^2.
143 m · The two semicircle ends join to form one full circle: π × 20 ≈ 62.8 m. Add the two straight sides, 40 + 40 = 80 m, for a total of about 143 m.
She used the diameter instead of the radius in the formula · The radius is half the diameter, 4 cm, so she should have squared 4, not 8. The correct area is about 50.24 cm².