# 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 (Mathematics Formula Sheet)

C = 2πr

C = πd

A = πr²

Formulas (NOT on Mathematics Formula Sheet)
d = 2r

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

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

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

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

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

9 centimeters

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

r = $\bf\displaystyle\frac{1}{2}\times18\$ = 9

Input Display Comment
1  2  x 18 $\bf\displaystyle\frac{1}{2}$*18 r = $\bf\displaystyle \frac{1}{2}d$
###### Circle

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

26 centimeters

d = 2r

d = 2 × 13 = 26

Input Display Comment
2 × 13 2*13 d = 2r
###### Circle

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

14π centimeters

C = 2πr
C = 2 × π × 7 = 14π

Input Display 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

Input Display 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 centimeters

C = πd
C = π × 24 = 24π

Input Display Comment
× 24 π*24 C = πd
###### Circle

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

3 centimeters

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

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

Input Display Comment
3    $\bf\displaystyle\frac{3\pi}{\pi }$ d = $\bf\displaystyle\frac{C}{\pi }$
###### Circle

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

1.5 centimeters

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

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

Input Display Comment
3  2  $\bf\displaystyle\frac{3\pi}{2\pi }$ r = $\bf\displaystyle\frac{C}{2\pi }$
$\bf\displaystyle\frac{3}{2}$
(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

Input Display Comment
× 7  π*7² A  =  πr²
###### Circle

Question

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

8 centimeters

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

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

Input Display Comment
64    $\bf\displaystyle\sqrt{\frac{64}{\pi }}$ r = $\bf\displaystyle\sqrt{\frac{A}{\pi }}$
###### Circle

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

144π square centimeters

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

r = $\bf\displaystyle\frac{1}{2}\times24\$ = 12

A = πr²
A = π × 12² = 144π

Input Display Comment
1  2  x 24 $\bf\displaystyle\frac{1}{2}$*24 r = $\bf\displaystyle \frac{1}{2}d$
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