Circle

Scott Solomon

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

circle


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?

Answer
9 centimeters

Answer Process
r = \bf\displaystyle \frac{1}{2}d

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

Input Display Comment
clear blinker clears screen
fraction 1 down 2 right x 18 \bf\displaystyle\frac{1}{2}*18 r = \bf\displaystyle \frac{1}{2}d
enter 9 Answer
Circle


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

Answer
26 centimeters

Answer Process
d = 2r
d = 2 × 13 = 26

Input Display Comment
clear blinker clears screen
2 × 13 2*13 d = 2r
enter 26 Answer
Circle


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

Answer
14π centimeters

Answer Process
C = 2πr
C = 2 × π × 7 = 14π

Input Display Comment
clear blinker clears screen
2 × π × 7 2*π*7 C = 2πr
enter 14π Answer
Circle


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

Answer
43.98229715

Answer Process
See Toggle.
14π ⇔ 43.98229715

Input Display Comment
clear blinker clears screen
2 × π × 7 2*π*7 C = 2πr
enter 14π
toggle 43.98229715 Answer
(Toggle)
Circle


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

Answer
44.0

Answer Process
See Rounding.
43.98229715 → 44.0


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

Answer
24π centimeters

Answer Process
C = πd
C = π × 24 = 24π

Input Display Comment
clear blinker clears screen
π × 24 π*24 C = πd
enter 24π Answer
Circle


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

Answer
3 centimeters

Answer Process
d = \bf\displaystyle\frac{C}{\pi }

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

Input Display Comment
clear blinker clears screen
fraction 3π down π right \bf\displaystyle\frac{3\pi}{\pi } d = \bf\displaystyle\frac{C}{\pi }
enter 3 Answer
Circle


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

Answer
1.5 centimeters

Answer Process
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
clear blinker clears screen
fraction 3π down 2π right \bf\displaystyle\frac{3\pi}{2\pi } r = \bf\displaystyle\frac{C}{2\pi }
enter \bf\displaystyle\frac{3}{2}
toggle 1.5 Answer
(Toggle)
Circle


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

Answer
A = 49π square centimeters

Answer Process
A = πr²
A = π × 7² = 49π

Input Display Comment
clear blinker clears screen
π × 7 square π*7² A  =  πr²
enter 49π Answer
Circle


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

Answer
8 centimeters

Answer Process
r = \bf\displaystyle\sqrt{\frac{A}{\pi }}

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

Input Display Comment
clear blinker clears screen
2nd square root fraction 64π down π right \bf\displaystyle\sqrt{\frac{64}{\pi }} r = \bf\displaystyle\sqrt{\frac{A}{\pi }}
enter 8 Answer
Circle


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

Answer
144π square centimeters

Answer Process
r = \bf\displaystyle \frac{1}{2}d

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

A = πr²
A = π × 12² = 144π

Input Display Comment
clear blinker clears screen
fraction 1 down 2 right x 24 \bf\displaystyle\frac{1}{2}*24 r = \bf\displaystyle \frac{1}{2}d
enter 12 r
π × 12 square π*12² A  =  πr²
enter 144π Answer
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?


Practice – Answers
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

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