Math with Mrs. Mandel: April 2016 - Free Printable

Let’s solve each circle problem step by step. We’ll use:

- Circumference (C) = π × d or C = 2 × π × r
- Area (A) = π × r²
- Use π = 3.14
- Round answers to the nearest hundredth if needed.

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Problem 1: Circle with diameter = 6 in → so radius r = 3 in

We are given:
- G: r = ___ in → r = 3
- C: C = ___ in → C = π × d = 3.14 × 6 = 18.84
- I: A = ___ in² → A = π × r² = 3.14 × 3² = 3.14 × 9 = 28.26

✔ So for #1:
G = 3, C = 18.84, I = 28.26

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Problem 2: Circle with radius = 2.6 m

We need:
- D: d = ___ m → d = 2 × r = 2 × 2.6 = 5.2
- O: C = ___ m → C = 2 × π × r = 2 × 3.14 × 2.6 = 6.28 × 2.6 = let’s calculate:
6.28 × 2 = 12.56; 6.28 × 0.6 = 3.768 → total = 12.56 + 3.768 = 16.328 → round to 16.33
- H: A = ___ m² → A = π × r² = 3.14 × (2.6)² = 3.14 × 6.76
Let’s compute: 3.14 × 6 = 18.84; 3.14 × 0.76 = ?
3.14 × 0.7 = 2.198; 3.14 × 0.06 = 0.1884 → total = 2.198 + 0.1884 = 2.3864
So total A = 18.84 + 2.3864 = 21.2264 → round to 21.23

✔ So for #2:
D = 5.2, O = 16.33, H = 21.23

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Problem 3: d = 80 ft → so r = 40 ft

We need:
- U: C = ___ ft → C = π × d = 3.14 × 80 = 251.2
- W: A = ___ ft² → A = π × r² = 3.14 × 40² = 3.14 × 1600 = 5024

✔ So for #3:
U = 251.2, W = 5024

*(Note: The worksheet says “S” and “K” but those belong to problem 4 — we’ll do them next)*

Wait — looking at the coded title section, letters are assigned per problem:

Problem 3 has:
C = ___ ft → that’s U? Wait no — let’s check the layout again.

Actually, looking at the worksheet:

For problem 3:
It says:
C = ___ ft → letter U
A = ___ ft² → letter W

But also there’s a “S” and “K” under problem 4? Let me re-read.

Actually, the problems are labeled:

1. → G, C, I
2. → D, O, H
3. → U, W *(and maybe S? No — wait, problem 4 starts with r=18 in → then it says S: d=___, L: C=___, K: A=___)*

Ah! I see — problem 3 is only two blanks? But in the image, problem 3 says:

> 3. d = 80 ft
> C = ___ ft → U
> A = ___ ft² → W

Then problem 4:

> 4. r = 18 in.
> S: d = ___ in.
> L: C = ___ in.
> K: A = ___ in.²

So yes — problem 3 gives us U and W.

We already did:

U = C = 3.14 × 80 = 251.2
W = A = 3.14 × 40² = 3.14 × 1600 = 5024

✔ Correct.

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Problem 4: r = 18 in → so d = 36 in

We need:
- S: d = ___ in → 36
- L: C = ___ in → C = 2 × π × r = 2 × 3.14 × 18 = 6.28 × 18
6 × 18 = 108; 0.28 × 18 = 5.04 → total = 113.04
- K: A = ___ in² → A = π × r² = 3.14 × 18² = 3.14 × 324
Let’s compute: 3 × 324 = 972; 0.14 × 324 = ?
0.1 × 324 = 32.4; 0.04 × 324 = 12.96 → total = 32.4 + 12.96 = 45.36
So A = 972 + 45.36 = 1017.36

✔ So for #4:
S = 36, L = 113.04, K = 1017.36

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Problem 5: d = 1.4 cm → so r = 0.7 cm

We need:
- E: r = ___ cm → 0.7
- T: C = ___ cm → C = π × d = 3.14 × 1.4 = ?
3.14 × 1 = 3.14; 3.14 × 0.4 = 1.256 → total = 4.396 → round to 4.40
- Q: A = ___ cm² → A = π × r² = 3.14 × (0.7)² = 3.14 × 0.49
3.14 × 0.5 = 1.57; minus 3.14 × 0.01 = 0.0314 → so 1.57 - 0.0314 = 1.5386 → better to compute directly:
3.14 × 0.49 = (3.14 × 49)/100 = 153.86 / 100 = 1.5386 → round to 1.54

✔ So for #5:
E = 0.7, T = 4.40, Q = 1.54

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Problem 6: r = 7.5 mm → so d = 15 mm

We need:
- F: d = ___ mm → 15
- N: C = ___ mm → C = 2 × π × r = 2 × 3.14 × 7.5 = 6.28 × 7.5
6 × 7.5 = 45; 0.28 × 7.5 = 2.1 → total = 47.1
- R: A = ___ mm² → A = π × r² = 3.14 × (7.5)² = 3.14 × 56.25
Let’s compute: 3 × 56.25 = 168.75; 0.14 × 56.25 = ?
0.1 × 56.25 = 5.625; 0.04 × 56.25 = 2.25 → total = 5.625 + 2.25 = 7.875
So A = 168.75 + 7.875 = 176.625 → round to 176.63

✔ So for #6:
F = 15, N = 47.1, R = 176.63

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Now, let’s collect all the letters and their corresponding numbers from the "CODED TITLE" box.

The coded title has two rows of numbers:

First row:
5.024, 176.63, 0.7, 40, 1,017.36, 0.7, 5.2, 4,954, 18.84, 47.1, 3, 113.04, 0.7, 1.69, 5.024, 28.26, 4.40, 21.23

Second row:
16.33, 47.1, 0.7, 172.39, 36, 1.54, 251.2, 18.84, 176.63, 0.7, 984.46, 15, 16.33, 16.33, 4.40

We now match each answer we found to these numbers and find which letter goes with which number.

From our solutions:

Problem 1:
G = 3 → look for 3 in code → first row: position 11 is “3” → letter above it? Wait — how is the coding done?

Looking at the worksheet: under each problem, they assign letters to the blanks. Then in the “CODED TITLE”, each number corresponds to a letter based on where it appears in the exercise.

Actually, the instruction says:
“Each time an answer appears in the coded title, write the letter of the exercise above it.”

So for example, if in problem 1, you got G = 3, and 3 appears in the coded title, then wherever 3 appears, you put G.

Similarly, C = 18.84 → so every 18.84 gets C.

I = 28.26 → every 28.26 gets I.

And so on.

So let’s list all our answers with their letters:

From Problem 1:
G = 3
C = 18.84
I = 28.26

Problem 2:
D = 5.2
O = 16.33
H = 21.23

Problem 3:
U = 251.2
W = 5024 → wait, 5024 is not in the coded title? Let me check.

Wait — in the coded title, I see 5.024 — that’s probably 5024 written as 5.024? Because 5024 1000 = 5.024 — likely a decimal placement error in printing? Or perhaps it's 5.024 meaning 5024? That doesn’t make sense.

Wait — let’s check problem 3: A = 5024 ft² — but in the coded title, we have 5.024 — that must be a typo or misprint. Probably it should be 5024, but written as 5.024 by mistake? Or perhaps we made a mistake?

Wait — no: 3.14 × 1600 = 5024 exactly. And in the coded title, first number is 5.024 — that’s 5024 divided by 1000. Maybe it’s a formatting issue — perhaps it’s meant to be 5024, but printed as 5.024? Or maybe we should treat 5.024 as representing 5024? That seems odd.

Alternatively, perhaps I miscalculated? Let me double-check problem 3 area:

d = 80 ft → r = 40 ft
A = πr² = 3.14 × 40 × 40 = 3.14 × 1600

3.14 × 1600:

3 × 1600 = 4800
0.14 × 1600 = 224
Total = 4800 + 224 = 5024 — correct.

But in the coded title, it’s written as 5.024 — which is 5024 / 1000. Perhaps it’s a decimal point error in the worksheet? Or maybe it’s intentional? Let’s see if other numbers match.

Look at problem 4: K = 1017.36 — and in coded title, we have 1,017.36 — yes, matches.

Problem 6: R = 176.63 — and in coded title, second row first number is 176.63 — matches.

Problem 1: I = 28.26 — in coded title, first row 16th number is 28.26 — matches.

Problem 2: H = 21.23 — first row last number is 21.23 — matches.

Problem 5: Q = 1.54 — second row 6th number is 1.54 — matches.

Problem 4: L = 113.04 — first row 12th number is 113.04 — matches.

Problem 5: T = 4.40 — first row 17th is 4.40, second row last is 4.40 — matches.

Problem 6: N = 47.1 — first row 10th is 47.1, second row 2nd is 47.1 — matches.

Problem 2: O = 16.33 — second row 1st is 16.33, also 13th and 14th are 16.33 — matches.

Problem 4: S = 36 — second row 5th is 36 — matches.

Problem 6: F = 15 — second row 12th is 15 — matches.

Problem 1: G = 3 — first row 11th is 3 — matches.

Problem 2: D = 5.2 — first row 7th is 5.2 — matches.

Problem 5: E = 0.7 — appears many times: first row 3rd, 6th, 13th; second row 3rd, 10th — all 0.7 — so E = 0.7.

Problem 3: U = 251.2 — second row 7th is 251.2 — matches.

Problem 3: W = 5024 — but in coded title, first number is 5.024 — this must be a typo. Probably it’s meant to be 5024, but written as 5.024. Since 5.024 is very close to 5024/1000, and no other number is near 5024, I think we should assume that 5.024 represents 5024 for coding purposes. Otherwise, W wouldn't appear anywhere.

Similarly, is there a 4954? First row 8th is 4,954 — what is that? Did we get 4954 anywhere?

Let me check — did any calculation give 4954? Not that I recall. Perhaps it’s from another problem? Or maybe it’s a distractor.

Wait — problem 3 area is 5024, and 4954 is close but not the same. Maybe I made a mistake?

Another thought: perhaps for problem 3, they want us to use r=40, but maybe they used π=3.1416 or something? But the instruction says use 3.14.

Perhaps 4954 is from a different interpretation. Let’s skip for now.

Also, in the coded title, there’s 1.69 — what is that? We didn’t get 1.69.

And 984.46 — not matching anything.

And 172.39 — not matching.

So some numbers may not correspond to our answers — perhaps they are red herrings, or for other problems.

But according to the instructions, we only use the answers we calculated.

So let’s map each number in the coded title to the letter based on our answers.

List of our answer-letter pairs:

- 3 → G
- 18.84 → C
- 28.26 → I
- 5.2 → D
- 16.33 → O
- 21.23 → H
- 251.2 → U
- 5024 → W (but coded as 5.024 — we'll assume 5.024 means W)
- 36 → S
- 113.04 → L
- 1017.36 → K
- 0.7 → E
- 4.40 → T and also Q? No — T is 4.40, Q is 1.54
Wait: T = 4.40, Q = 1.54
- 1.54 → Q
- 15 → F
- 47.1 → N
- 176.63 → R

Also, from problem 5: E = 0.7, T = 4.40, Q = 1.54

Now, let’s go through the coded title row by row and replace each number with its letter.

First row of coded title:

Positions (let's index them):

1: 5.024 → assume this is 5024 → W
2: 176.63 → R
3: 0.7 → E
4: 40 → ? We don’t have 40 as an answer. What is 40? In problem 3, r=40, but we didn’t assign a letter to r=40 — only to C and A. So 40 might not correspond to any letter. But the instruction says "each time an answer appears", so if 40 is not one of our calculated answers (like circumference or area), then it shouldn’t be replaced. But in the context, perhaps it is? Let’s see.

In problem 3, we have d=80, r=40, but the blanks are for C and A, not for r. So r=40 is not an answer we wrote down for a blank — so probably 40 does not correspond to any letter. Similarly, 1 is not an answer, etc.

This is confusing. Perhaps only the numbers that match our calculated circumferences and areas should be replaced, and others are left as is? But the title is supposed to spell out words.

Maybe I missed some assignments.

Let’s list all the blanks and their letters from the worksheet:

Problem 1:
G: r = 3 in → so G corresponds to 3
C: C = 18.84 in → C corresponds to 18.84
I: A = 28.26 in² → I corresponds to 28.26

Problem 2:
D: d = 5.2 m → D corresponds to 5.2
O: C = 16.33 m → O corresponds to 16.33
H: A = 21.23 m² → H corresponds to 21.23

Problem 3:
U: C = 251.2 ft → U corresponds to 251.2
W: A = 5024 ft² → W corresponds to 5024

Problem 4:
S: d = 36 in → S corresponds to 36
L: C = 113.04 in → L corresponds to 113.04
K: A = 1017.36 in² → K corresponds to 1017.36

Problem 5:
E: r = 0.7 cm → E corresponds to 0.7
T: C = 4.40 cm → T corresponds to 4.40
Q: A = 1.54 cm² → Q corresponds to 1.54

Problem 6:
F: d = 15 mm → F corresponds to 15
N: C = 47.1 mm → N corresponds to 47.1
R: A = 176.63 mm² → R corresponds to 176.63

So the values that should be replaced are:

3, 18.84, 28.26, 5.2, 16.33, 21.23, 251.2, 5024, 36, 113.04, 1017.36, 0.7, 4.40, 1.54, 15, 47.1, 176.63

Now, in the coded title, we have:

First row:
5.024, 176.63, 0.7, 40, 1,017.36, 0.7, 5.2, 4,954, 18.84, 47.1, 3, 113.04, 0.7, 1.69, 5.024, 28.26, 4.40, 21.23

Second row:
16.33, 47.1, 0.7, 172.39, 36, 1.54, 251.2, 18.84, 176.63, 0.7, 984.46, 15, 16.33, 16.33, 4.40

Now, let's replace each occurrence of our answer-values with their letters.

Start with first row:

1. 5.024 → assume this is 5024 → W
2. 176.63 → R
3. 0.7 → E
4. 40 → not in our list → leave as 40? But that would break the word. Perhaps 40 is meant to be something else? Or maybe it's a space? Unlikely. Another idea: in problem 3, r=40, and although not a blank, perhaps it's included? But the instruction says "each time an answer appears in the coded title, write the letter of the exercise above it" — and "answer" refers to the values we calculated for the blanks. So 40 is not an answer we calculated for a blank — so it should not be replaced. But then the title will have numbers in it, which is odd.

Perhaps for problem 3, they consider r=40 as part of the answer? But the blank is for C and A, not for r.

Let's look at the worksheet again mentally: in problem 3, it says "d = 80 ft" then below "C = ___ ft" with U, and "A = ___ ft²" with W. So only U and W are to be filled. So r=40 is not an answer for a blank.

Similarly, in problem 4, r=18 in is given, not asked for.

So probably, 40, 1, 1.69, 4954, 172.39, 984.46 are not to be replaced — they are either errors or distractors.

But then the coded title will have numbers, and the title won't spell correctly.

Perhaps 5.024 is meant to be 5024, and 4,954 is 4954, but we don't have 4954.

Another possibility: in problem 3, if they used π=3.14, A=5024, but perhaps they expect us to use more precise π? But the instruction says use 3.14.

Or perhaps for problem 3, A = πr^2 = 3.14 * 40*40 = 5024, but in the coded title, 5.024 is listed, which is 5024/1000, so maybe it's a decimal shift, and we should still use W for 5.024.

Similarly, 4,954 might be for another calculation.

Let's calculate what 4954 could be. If r=40, A= πr^2, if π=3.14, it's 5024. If π=3.1416, 3.1416*1600=5026.56, not 4954. If d=80, C=πd=3.14*80=251.2, not 4954.

Perhaps it's for a different circle. Or maybe it's a typo, and it's 5024 written as 4954 by mistake.

Notice that 5024 and 4954 are close; perhaps it's a misprint, and it should be 5024.

Similarly, 1.69 — what is that? 1.3^2 = 1.69, but not related.

984.46 — not familiar.

172.39 — not familiar.

So perhaps only the numbers that match our answers should be replaced, and the others are ignored or are spaces.

But let's try to replace what we can and see what word forms.

First row:

1. 5.024 → W (assuming it's 5024)
2. 176.63 → R
3. 0.7 → E
4. 40 → ? let's skip for now, or perhaps it's ' ' (space)
5. 1,017.36 → K
6. 0.7 → E
7. 5.2 → D
8. 4,954 → ? not matched
9. 18.84 → C
10. 47.1 → N
11. 3 → G
12. 113.04 → L
13. 0.7 → E
14. 1.69 → ? not matched
15. 5.024 → W
16. 28.26 → I
17. 4.40 → T
18. 21.23 → H

So first row becomes: W, R, E, ?, K, E, D, ?, C, N, G, L, E, ?, W, I, T, H

If we ignore the unmatched numbers or treat them as spaces, it might be "WRE KED CNGLE WITH" — not good.

Perhaps 40 is 'O' or something, but we have O for 16.33.

Another idea: in the coded title, the numbers are to be matched to the answers, and if a number appears that is not an answer, it might be a separator or error.

But let's look at the second row:

1. 16.33 → O
2. 47.1 → N
3. 0.7 → E
4. 172.39 → ? not matched
5. 36 → S
6. 1.54 → Q
7. 251.2 → U
8. 18.84 → C
9. 176.63 → R
10. 0.7 → E
11. 984.46 → ? not matched
12. 15 → F
13. 16.33 → O
14. 16.33 → O
15. 4.40 → T

So second row: O, N, E, ?, S, Q, U, C, R, E, ?, F, O, O, T

Still messy.

Perhaps the unmatched numbers are to be ignored, and the letters form words when concatenated.

Let me try to write the letters in order, skipping unmatched numbers.

First row positions with matches:

1: W
2: R
3: E
5: K
6: E
7: D
9: C
10: N
11: G
12: L
13: E
15: W
16: I
17: T
18: H

So: W,R,E,K,E,D,C,N,G,L,E,W,I,T,H — that's "WREKEDCNGLEWITH" — not good.

Perhaps the numbers are to be read as they are, and the letters are placed above them, but the title is formed by the sequence of letters corresponding to the numbers in order.

Another approach: perhaps the "coded title" is a grid, and each number corresponds to a letter, and we need to output the letters in the order of the numbers, but only for the numbers that match our answers.

But the instruction says: "Each time an answer appears in the coded title, write the letter of the exercise above it."

So for each occurrence of a number in the coded title that matches one of our answers, we write the corresponding letter.

Then the title is the sequence of those letters in the order they appear in the coded title.

So let's list the coded title numbers in order, and for each, if it matches an answer, output the letter, else output nothing or skip.

But then the title might have gaps.

Perhaps the unmatched numbers are not part of the title, or are spaces.

Let's list the coded title as a single sequence:

Row 1: 5.024, 176.63, 0.7, 40, 1017.36, 0.7, 5.2, 4954, 18.84, 47.1, 3, 113.04, 0.7, 1.69, 5.024, 28.26, 4.40, 21.23

Row 2: 16.33, 47.1, 0.7, 172.39, 36, 1.54, 251.2, 18.84, 176.63, 0.7, 984.46, 15, 16.33, 16.33, 4.40

Now, for each, if it matches an answer, output the letter:

1. 5.024 → W (assume 5024)
2. 176.63 → R
3. 0.7 → E
4. 40 → no match → skip or space
5. 1017.36 → K
6. 0.7 → E
7. 5.2 → D
8. 4954 → no match → skip
9. 18.84 → C
10. 47.1 → N
11. 3 → G
12. 113.04 → L
13. 0.7 → E
14. 1.69 → no match → skip
15. 5.024 → W
16. 28.26 → I
17. 4.40 → T
18. 21.23 → H
19. 16.33 → O
20. 47.1 → N
21. 0.7 → E
22. 172.39 → no match → skip
23. 36 → S
24. 1.54 → Q
25. 251.2 → U
26. 18.84 → C
27. 176.63 → R
28. 0.7 → E
29. 984.46 → no match → skip
30. 15 → F
31. 16.33 → O
32. 16.33 → O
33. 4.40 → T

So the sequence of letters is:

W, R, E, [skip], K, E, D, [skip], C, N, G, L, E, [skip], W, I, T, H, O, N, E, [skip], S, Q, U, C, R, E, [skip], F, O, O, T

If we remove the skips, we get: WREKEDCNGLEWITHONESQUCREFOOT — still not good.

Perhaps the skips are spaces, so:

W R E K E D C N G L E W I T H O N E S Q U C R E F O O T

That looks like "WRE KED CNGLE WITH ONE SQU CRE FOOT" — not quite.

"WRE" might be "ARE", but we have W.

Another idea: perhaps 5.024 is not W, but something else. Or perhaps for problem 3, A = 5024, but in the coded title, it's 5.024, and we should use it as is, but then it doesn't match.

Let's check if 5.024 corresponds to any other answer. For example, in problem 5, A = 1.54, not 5.024.

Perhaps it's a different calculation.

Let's calculate the area for problem 3 with r=40, but using π=3.14, it's 5024, as before.

Perhaps the 5.024 is for a different unit, but unlikely.

Another thought: in the coded title, "5.024" might be "5024" with a decimal error, and "4,954" might be "4954", but we don't have 4954.

Let's calculate what 4954 could be. If d=80, C=πd=3.14*80=251.2, not 4954. If r=40, A=πr^2=5024. If they used π=3.14, but perhaps for circumference in inches or something.

Perhaps for problem 4, if r=18, A=3.14*324=1017.36, which is there.

Let's notice that in the first row, after 5.2, there is 4,954, then 18.84, etc.

Perhaps 4,954 is a typo for 5,024, and it's repeated.

Or perhaps it's 4954 for a different reason.

Let's try to see if 4954 matches any calculation. Suppose for problem 3, if they used r=40, but A = πr^2 = 3.14*1600=5024, or if they used d=80, C=251.2.

Another idea: perhaps "4,954" is "4954" and it's for the area of a circle with r=39.6 or something, but not likely.

Perhaps it's 5024 written as 4954 by mistake, and we should use W for both 5.024 and 4,954.

Let's assume that 4,954 is a typo and should be 5,024, so W.

Similarly, 1.69 might be 1.54 or something, but 1.54 is Q.

1.69 is 1.3^2, not related.

984.46 — not familiar.

172.39 — not familiar.

So let's assume that 4,954 is meant to be 5,024, so W.

Then in first row, position 8: 4,954 → W

Position 14: 1.69 → still not matched.

Position 22: 172.39 → not matched.

Position 29: 984.46 → not matched.

So with that, first row:

1. 5.024 → W
2. 176.63 → R
3. 0.7 → E
4. 40 → ?
5. 1017.36 → K
6. 0.7 → E
7. 5.2 → D
8. 4954 → W (assumed)
9. 18.84 → C
10. 47.1 → N
11. 3 → G
12. 113.04 → L
13. 0.7 → E
14. 1.69 → ?
15. 5.024 → W
16. 28.26 → I
17. 4.40 → T
18. 21.23 → H

So letters: W,R,E,?,K,E,D,W,C,N,G,L,E,?,W,I,T,H

If we take ? as space, then "WRE KEDWCNGLE WITH" — still not good.

Perhaps 40 is 'O', but we have O for 16.33.

Another idea: in problem 2, d=5.2, but perhaps they have a blank for r or something, but no.

Let's look back at the worksheet description. In the user's image, there is handwritten notes, but we are to solve based on the printed content.

Perhaps for problem 3, the "C = ___ ft" is U, "A = ___ ft²" is W, but also there is "S" and "K" for problem 4, etc.

Let's try to see the intended title. Common titles for such worksheets are like "Circle Magic" or "Pi Day" etc.

Perhaps the title is "WORK SHEET" or something.

Let's list the letters we have in order, and see if we can group them.

From the sequence, if we take only the matched letters in order:

From row 1: W,R,E,K,E,D,W,C,N,G,L,E,W,I,T,H

From row 2: O,N,E,S,Q,U,C,R,E,F,O,O,T

So combined: W,R,E,K,E,D,W,C,N,G,L,E,W,I,T,H,O,N,E,S,Q,U,C,R,E,F,O,O,T

Now, let's try to split into words:

WRE KED WC NGLE WITH ONE SQUCRE FOOT — not good.

"WRE" might be "ARE", but W is for 5024.

Perhaps 5.024 is not W, but let's see what else it could be.

Another thought: in problem 3, A = 5024, but perhaps they want it as 5.024 thousand, but still.

Perhaps the coded title has numbers that are the answers, and we need to output the letter for each, and the title is the string of letters.

But