Circle

Circle = Flat Round Shape with All Rim Points Equidistant from Center

Basics
r = Radius = distance from rim to center
d = Diameter = distance all the way across circle through its center
C = Circumference = distance around rim
A = Area = area covering surface of circle (measured in square units)

A circle occupies 360°.

π = pi
π = approximately 3.141592654 = approximately 3.14
π = ratio of a circle’s circumference to its diameter
π is primarily a multiplier.

When π is immediately adjacent to a number, letter, or parenthesis, an invisible multiplication sign is in force.
2π= 2 × π
πd = π × d
2(π) = 2 × π
π(d) = π × d

Formulas provided by Mathematics Formula Sheet)

C = 2πr

C = πd

A = πr²

Formulas (NOT provided by Mathematics Formula Sheet)
d = 2r

$\bf\displaystyle r=\frac{1}{2}d$

$\bf\displaystyle d=\frac{C}{\pi }$

$\bf\displaystyle r=\frac{C}{2\pi }$

$\bf\displaystyle r=\sqrt{\frac{A}{\pi }}$

Question
A circle has a diameter of 18 centimeters.  What is its radius?

9 centimeters

$\bf\displaystyle r=\frac{1}{2}d$

$\bf\displaystyle r=\frac{1}{2}\times 18$ = 9

Calculator Click What You See Comment
1  2  × 18 $\bf\displaystyle r=\frac{1}{2}\times 18$ $\bf\displaystyle r=\frac{1}{2}d$
9 r
Circle

Question
A circle has a radius of 13 centimeters.  What is its diameter?

26 centimeters

d = 2r
d = 2 × 13 = 26

Calculator Click What You See Comment
2 × 13 2*13 d = 2r
26 d
Circle

Question
A coin has a radius of 7 centimeters.  What is its circumference?

14π centimeters

C = 2πr
C = 2 × π × 7 = 14π

Calculator Click What You See Comment
2 ×  × 7 2*π*7 C = 2πr
Circle

Question
With reference to the question above, what is the circumference of the coin in decimal terms?

43.98229715

See Toggle.
14π ⇔ 43.98229715

Calculator Click What You See Comment
2 ×  × 7 2*π*7 C = 2πr
14π
(Toggle)
Circle

Question
With reference to the question above, what is the circumference of the coin to the nearest tenth of a centimeter?

44.0

See Rounding.
43.98229715  44.0

Question
An earring has a diameter of 24 centimeters.  What is its circumference?

24π

C = πd
C = π × 24 = 24π

Calculator Click What You See Comment
× 24 π*24 C = πd
Circle

Question
A coin has a circumference of 3π centimeters.  What is its diameter?

3 centimeters

$\bf\displaystyle d=\frac{C}{\pi }$

d = $\bf\displaystyle\frac{3\pi}{\pi}$ = 3

Calculator Click What You See Comment
3    $\bf\displaystyle\frac{3\pi}{\pi}$ $\bf\displaystyle d=\frac{C}{\pi }$
Circle

Question
A coin has a circumference of 3π centimeters.  What is its radius in decimal terms?

1.5 centimeters

$\bf\displaystyle r=\frac{C}{2\pi }$

r = $\bf\displaystyle\frac{3\pi}{2\pi}$$\bf\displaystyle\frac{3}{2}$ = 1.5 after toggle

Calculator Click What You See Comment
3  2  $\bf\displaystyle\frac{3\pi}{2\pi}$ $\bf\displaystyle r=\frac{C}{2\pi }$
$\bf\displaystyle\frac{3}{2}$
(Toggle)
Circle

Question
A coin has a radius of 7 centimeters.  What is its area?

A = 49π square centimeters

A = πr²
A = π × 7² = 49π

Calculator Click What You See Comment
× 7  π*7² A  =  πr²
Circle

Question

A coin has an area of 64π square centimeters.  What is its radius?

8 centimeters

$\bf\displaystyle r=\sqrt{\frac{A}{\pi }}$

r = $\bf\displaystyle \sqrt{\frac{64\pi}{\pi }}$ = 8

Calculator Click What You See Comment
64    $\bf\displaystyle \sqrt{\frac{64\pi}{\pi }}$ $\bf\displaystyle r=\sqrt{\frac{A}{\pi }}$
Circle

Question
An earring has a diameter of 24 centimeters.  What is its area?

144π square centimeters

$\bf\displaystyle r=\frac{1}{2}d$

$\bf\displaystyle r=\frac{1}{2}\times 24$ = 12

A = πr²
A = π × 12² = 144π

Calculator Click What You See Comment
1  2  × 24 $\bf\displaystyle r=\frac{1}{2}\times 24$ $\bf\displaystyle r=\frac{1}{2}d$
12 r
× 12  π*12² A  =  πr²
Circle

Practice – Questions
1.  A circle has a diameter of 22 centimeters.  What is its radius?

2.  A circle has a radius of 14 centimeters.  What is its diameter?

3.  A pizza has a radius of 6 inches.  What is its circumference?

4.  With reference to Question 3, what is the circumference of the pizza in decimal terms?

5.  With reference to Question 3, what is the circumference of the pizza rounded to the nearest hundredth of an inch?

6.  A pizza has a diameter of 14 inches.  What is its circumference?

7.  A pizza has a circumference of 4π inches.  What is its diameter?

8.  A pizza has a circumference of 7π inches.  What is its radius in decimal terms?

9.  A pizza has a radius of 6 inches.  What is its area?

10.  A pizza has a diameter of 16 inches.  What is its area?

1.  11 centimeters

2.  28 centimeters

3.  12π inches

4.  37.69911184 inches

5.  37.70 inches

6.  14π inches

7.  4 inches

8.  3.5 inches

9.  36π square inches

10.  64π square inches