Question

find the circumference of each circle to help crack the code and did you know? question below (answers to 1dp).
circles labeled a to π with diameters or radii:
a: diameter 5; b: diameter 8; c: diameter 3.7; d: diameter 11; e: diameter 16; f: diameter 2.9;
g: radius 6; h: radius 9; i: radius 8.2; j: radius 4.4; k: radius 12; l: radius 7.5;
m: diameter 10.5; n: radius 10; o: radius 9.3; p: diameter 17; q: radius 15; r: diameter 15.7;
s: radius 1.8; t: radius 11.5; u: diameter 25; v: diameter 17.4; w: diameter 23.8; x: radius 2.1;
y: diameter 19; z: radius 16; π: diameter 27.
did you know...? section with π symbol and numbers 15.7, 62.8 in a grid.

Explanation:

The circumference of a circle is calculated using two formulas:
- If given diameter \(d\): \(C = \pi d\)
- If given radius \(r\): \(C = 2\pi r\)
We use \(\pi \approx 3.1416\) and round to 1 decimal place.

Step1: Calculate Circumference for A

Diameter \(d=5\), so \(C = \pi \times 5\)
\(C \approx 3.1416 \times 5 = 15.7\)

Step2: Calculate Circumference for B

Diameter \(d=8\), so \(C = \pi \times 8\)
\(C \approx 3.1416 \times 8 = 25.1\)

Step3: Calculate Circumference for C

Diameter \(d=3.7\), so \(C = \pi \times 3.7\)
\(C \approx 3.1416 \times 3.7 = 11.6\)

Step4: Calculate Circumference for D

Diameter \(d=11\), so \(C = \pi \times 11\)
\(C \approx 3.1416 \times 11 = 34.6\)

Step5: Calculate Circumference for E

Diameter \(d=16\), so \(C = \pi \times 16\)
\(C \approx 3.1416 \times 16 = 50.3\)

Step6: Calculate Circumference for F

Diameter \(d=2.9\), so \(C = \pi \times 2.9\)
\(C \approx 3.1416 \times 2.9 = 9.1\)

Step7: Calculate Circumference for G

Radius \(r=6\), so \(C = 2\pi \times 6\)
\(C \approx 2 \times 3.1416 \times 6 = 37.7\)

Step8: Calculate Circumference for H

Radius \(r=9\), so \(C = 2\pi \times 9\)
\(C \approx 2 \times 3.1416 \times 9 = 56.5\)

Step9: Calculate Circumference for I

Radius \(r=8.2\), so \(C = 2\pi \times 8.2\)
\(C \approx 2 \times 3.1416 \times 8.2 = 51.5\)

Step10: Calculate Circumference for J

Radius \(r=4.4\), so \(C = 2\pi \times 4.4\)
\(C \approx 2 \times 3.1416 \times 4.4 = 27.6\)

Step11: Calculate Circumference for K

Radius \(r=12\), so \(C = 2\pi \times 12\)
\(C \approx 2 \times 3.1416 \times 12 = 75.4\)

Step12: Calculate Circumference for L

Radius \(r=7.5\), so \(C = 2\pi \times 7.5\)
\(C \approx 2 \times 3.1416 \times 7.5 = 47.1\)

Step13: Calculate Circumference for M

Diameter \(d=20.5\), so \(C = \pi \times 20.5\)
\(C \approx 3.1416 \times 20.5 = 64.4\)

Step14: Calculate Circumference for N

Radius \(r=10\), so \(C = 2\pi \times 10\)
\(C \approx 2 \times 3.1416 \times 10 = 62.8\)

Step15: Calculate Circumference for O

Radius \(r=9.3\), so \(C = 2\pi \times 9.3\)
\(C \approx 2 \times 3.1416 \times 9.3 = 58.4\)

Step16: Calculate Circumference for P

Diameter \(d=17\), so \(C = \pi \times 17\)
\(C \approx 3.1416 \times 17 = 53.4\)

Step17: Calculate Circumference for Q

Radius \(r=15\), so \(C = 2\pi \times 15\)
\(C \approx 2 \times 3.1416 \times 15 = 94.2\)

Step18: Calculate Circumference for R

Diameter \(d=15.7\), so \(C = \pi \times 15.7\)
\(C \approx 3.1416 \times 15.7 = 49.3\)

Step19: Calculate Circumference for S

Radius \(r=1.8\), so \(C = 2\pi \times 1.8\)
\(C \approx 2 \times 3.1416 \times 1.8 = 11.3\)

Step20: Calculate Circumference for T

Radius \(r=11.5\), so \(C = 2\pi \times 11.5\)
\(C \approx 2 \times 3.1416 \times 11.5 = 72.3\)

Step21: Calculate Circumference for U

Diameter \(d=25\), so \(C = \pi \times 25\)
\(C \approx 3.1416 \times 25 = 78.5\)

Step22: Calculate Circumference for V

Diameter \(d=17.4\), so \(C = \pi \times 17.4\)
\(C \approx 3.1416 \times 17.4 = 54.7\)

Step23: Calculate Circumference for W

Diameter \(d=23.8\), so \(C = \pi \times 23.8\)
\(C \approx 3.1416 \times 23.8 = 74.8\)

Step24: Calculate Circumference for X

Radius \(r=2.1\), so \(C = 2\pi \times 2.1\)
\(C \approx 2 \times 3.1416 \times 2.1 = 13.2\)

Step25: Calculate Circumference for Y

Diameter \(d=19\), so \(C = \pi \times 19\)
\(C \approx 3.1416 \times 19 = 59.7\)

Step26: Calculate Circumference for Z

Radius \(r=16\), so \(C = 2\pi \times 16\)
\(C \approx 2 \times 3.1416 \times 16 = 100.5\)

Step27: Calculate Circumference for π

Diameter \(d=27\), so \(C = \pi \times 27\)
\(C \approx 3.1416 \times 27 = 84.8\)

Answer:

Circle	Circumference (1 d.p.)
B	25.1
C	11.6
D	34.6
E	50.3
F	9.1
G	37.7
H	56.5
I	51.5
J	27.6
K	75.4
L	47.1
M	64.4
N	62.8
O	58.4
P	53.4
Q	94.2
R	49.3
S	11.3
T	72.3
U	78.5
V	54.7
W	74.8
X	13.2
Y	59.7
Z	100.5
π	84.8

The two values in the "Did you know..." box match the circumferences of A (15.7) and N (62.8).