Math with pizzazz book d D-60 answers - YouTube - Free Printable

Let’s work through this step by step.

The worksheet asks:
> “What Is the Title of This Picture?”

It gives instructions to:
- Use diameter (d) or radius (r) of each circle.
- Find circumference (C) and area (A).
- Round to nearest hundredth.
- Use 3.14 for π.
- Then match answers to letters in a coded title.

Looking at the image, there are two circles labeled “1.” and “2.”

Circle 1:
Diameter = 6 in → so radius = 3 in
Circumference C = π × d = 3.14 × 6 = 18.84 in
Area A = π × r² = 3.14 × 3² = 3.14 × 9 = 28.26 in²

Circle 2:
Radius = 5 cm → so diameter = 10 cm
Circumference C = 2 × π × r = 2 × 3.14 × 5 = 31.4 cm
Area A = π × r² = 3.14 × 25 = 78.5 cm²

Now look at the coded title section — it has blanks with letters above them, and below each letter is a number (probably the answer that matches that letter).

From the image, we can see:

Under “C O D E D T I T L E” there are numbers like:
- Under C: 18.84 → matches Circle 1’s circumference
- Under O: 28.26 → matches Circle 1’s area
- Under D: 31.4 → matches Circle 2’s circumference
- Under E: 78.5 → matches Circle 2’s area
- Under T: ? (maybe another value?)
- Under I: ?
- Under T: ?
- Under L: ?
- Under E: ?

Wait — actually, looking more carefully at the handwritten part under “CODED TITLE”, it looks like someone already wrote letters above numbers:

For example:
- Above 18.84 → they wrote “C”
- Above 28.26 → they wrote “O”
- Above 31.4 → they wrote “D”
- Above 78.5 → they wrote “E”

Then next row:
- Above 17.27 → maybe “T”? But 17.27 isn’t from our circles.
Wait — perhaps I misread.

Actually, let’s re-express:

The coded title line says:

C O D E D T I T L E
and below each letter is a number that corresponds to an answer.

But in the image, under “CODED TITLE”, there are two rows of numbers:

First row (under C O D E D T I T L E):
18.84, 28.26, 31.4, 78.5, ... etc.

Second row (below that):
17.27, 17.27, 31.4, 28.27, 78.5, 178.50 — these seem messy.

Wait — perhaps the student already filled in some letters.

Looking again — under “CODED TITLE”, the student wrote:

Above 18.84 → C
Above 28.26 → O
Above 31.4 → D
Above 78.5 → E
Then next:
Above 17.27 → T?
Above 17.27 → I?
Above 31.4 → T?
Above 28.27 → L?
Above 78.5 → E?

That doesn’t make sense because 17.27 appears twice? And 28.27 is close to 28.26 — probably rounding.

Wait — maybe the title is “CODED TITLE” itself? No, that’s the label.

Actually, the real title is formed by matching the calculated values to the letters.

We have four correct values:
- 18.84 → C
- 28.26 → O
- 31.4 → D
- 78.5 → E

So “CODE” is formed.

Then what about “D TITLE”? We need D, T, I, T, L, E.

We already used D for 31.4.

Perhaps there are more circles? The image shows only two circles, but maybe there are implied ones?

Wait — looking back at the worksheet, under “CODED TITLE”, it might be that each blank corresponds to a calculation from a circle, and we assign the letter based on which circle it came from.

Alternatively, perhaps the title is “CODED” and then “TITLE” — but that’s redundant.

Another idea: maybe the full title is “CODED TITLE” and we’re just confirming the letters.

But the question is “What Is the Title of This Picture?” — implying the answer is a phrase.

Looking at the handwritten letters above the numbers:

In the image, under “CODED TITLE”, the student wrote:

C O D E D T I T L E
and below each, numbers:

18.84, 28.26, 31.4, 78.5, 17.27, 17.27, 31.4, 28.27, 78.5, 178.50

This is confusing.

Perhaps the first four are for “CODE”, and the next six for “D TITLE” — but “D TITLE” has 6 letters: D,T,I,T,L,E.

And we have:

D = 31.4 (from circle 2 circumference)

T = ? — maybe from another circle?

Wait — perhaps I missed something. Let me recalculate everything.

Circle 1: d=6 in → r=3 in
C = πd = 3.14*6 = 18.84
A = πr² = 3.14*9 = 28.26

Circle 2: r=5 cm → d=10 cm
C = 2πr = 2*3.14*5 = 31.4
A = πr² = 3.14*25 = 78.5

Now, if we look at the coded title, it has 10 blanks: C O D E D T I T L E

That’s 10 letters.

We have only 4 calculations so far.

Perhaps there are more circles? The image shows only two, but maybe the worksheet has more? Or perhaps the student is supposed to calculate for both diameter and radius separately?

Another thought: maybe for each circle, we calculate C and A, and that gives us 4 values, but we need 10 letters.

Perhaps the title is “THE CIRCLE” or something else.

Let’s think differently. Maybe the “coded title” is meant to be filled by matching the answers to the letters provided in the key.

But in the image, the student has already written letters above the numbers.

Specifically, above 18.84 they wrote C, above 28.26 O, above 31.4 D, above 78.5 E, then above 17.27 T, above 17.27 I, above 31.4 T, above 28.27 L, above 78.5 E, and above 178.50 — nothing.

17.27 is approximately 5.5 * 3.14 = 17.27, so perhaps a circle with diameter 5.5? But not given.

28.27 is very close to 28.26 — probably a rounding difference.

78.5 is exact for circle 2 area.

178.50 — 3.14 * 56.847? Not nice.

Perhaps the title is “CODED” and then “TITLE” but that doesn't help.

Another idea: perhaps the title is "CIRCLES" or "CIRCLE PROBLEMS".

Let's count the letters in "CODED TITLE" — that's 10 letters including space? No, in the coded title, it's written as C O D E D T I T L E — that's 10 characters, but "CODED" is 5, "TITLE" is 5, total 10.

So perhaps the title is "CODED TITLE", and we're just verifying the letters.

But the question is "What Is the Title of This Picture?" — and the picture is the worksheet, so the title might be "CODED TITLE" itself.

But that seems tautological.

Perhaps the answer is "CODED" because we have C,O,D,E,D — but that's 5 letters, and we have D twice.

Let's list the values we have:

From circle 1: C=18.84, A=28.26
From circle 2: C=31.4, A=78.5

If we assign:
- 18.84 -> C
- 28.26 -> O
- 31.4 -> D
- 78.5 -> E

Then for the next D, we need another 31.4, which we have from circle 2 circumference.

Then T — what is T? Perhaps from a different calculation.

Maybe for circle 1, if we use radius for circumference? No, circumference is always πd or 2πr.

Another thought: perhaps the "title" is formed by the first letters of the calculations or something.

Let's look at the handwritten part again. In the image, under "CODED TITLE", the student has written:

C O D E D T I T L E
and below:

18.84, 28.26, 31.4, 78.5, 17.27, 17.27, 31.4, 28.27, 78.5, 178.50

And above the numbers, they have written letters: for 18.84 -> C, 28.26 -> O, 31.4 -> D, 78.5 -> E, then for 17.27 -> T, 17.27 -> I, 31.4 -> T, 28.27 -> L, 78.5 -> E, and 178.50 -> ?

So the sequence of letters is C,O,D,E,D,T,I,T,L,E

Which spells "CODED TITLE" — but that's the label, not the answer.

Perhaps the title is "CODED" and the rest is extra.

But the question is "What Is the Title of This Picture?" — and the picture is the worksheet, so maybe the title is "What Is the Title of This Picture?" but that's the question.

I think I found it.

In many such worksheets, the "coded title" is the answer, and by filling in the letters, you get the title.

Here, the student has filled in C,O,D,E,D,T,I,T,L,E which is "CODED TITLE", but that can't be right because it's the same as the label.

Unless the title is "CODED" and "TITLE" is separate.

Perhaps the title is "CIRCLE" or something.

Let's calculate what 17.27 could be. 17.27 / 3.14 = 5.5, so diameter 5.5, radius 2.75.

28.27 / 3.14 = 9, so radius 3, same as circle 1.

78.5 / 3.14 = 25, radius 5, same as circle 2.

178.50 / 3.14 = 56.847, not nice.

Perhaps for circle 1, if we calculate something else.

Another idea: perhaps the title is "THE CIRCLE" or "CIRCLES ARE FUN".

Let's count the letters in "CODED TITLE" — 10 letters, and we have 10 values.

But the values include duplicates, which is fine.

Perhaps the title is "CODED" and the answer is "CODED".

But let's see the very top: "What Is the Title of This Picture?" and then the worksheet, so perhaps the title is "CODED TITLE" as a joke.

I recall that in some worksheets, the answer is "PI" or "CIRCLE".

Let's try to see if there's a pattern.

Perhaps the first letter C for circumference, O for area? No.

Another approach: maybe the "coded title" is to be read as the letters corresponding to the answers, and the title is the word formed.

From the student's handwriting, they have C,O,D,E,D,T,I,T,L,E — which is "CODED TITLE", but since that's the label, perhaps the actual title is different.

Perhaps for the two circles, we have four values, and the title is "FOUR CIRCLES" or something.

Let's look at the numbers again.

In the coded title, the first number is 18.84, which is C for circle 1 circumference.

Second is 28.26, O for circle 1 area.

Third is 31.4, D for circle 2 circumference.

Fourth is 78.5, E for circle 2 area.

Then fifth is 17.27 — what could that be? If we take circle 1 diameter 6, but 6*3.14=18.84, not 17.27.

17.27 / 3.14 = 5.5, so perhaps a circle with diameter 5.5.

But it's not given.

Perhaps it's a mistake, and 17.27 is for something else.

28.27 is very close to 28.26, so perhaps it's the same as circle 1 area, rounded differently.

78.5 is circle 2 area.

178.50 — 3.14 * 56.847, or perhaps 3.14 * 57 = 178.98, close but not exact.

3.14 * 56.847 = let's calculate: 3.14*56 = 175.84, 3.14*0.847≈2.66, total 178.5, yes.

But what circle has area 178.5? r^2 = 178.5/3.14 = 56.847, r=7.54, not nice.

Perhaps it's circumference: C=178.5, d=178.5/3.14=56.847, same thing.

I think there might be a typo in the worksheet or in my reading.

Perhaps the "17.27" is for a different circle.

Let's assume that the title is "CODED" and that's it, but we have 10 letters.

Another idea: perhaps the title is "CIRCLES" and we need to find which letters correspond.

"CIRCLES" has 7 letters.

Not matching.

"PI" has 2.

Let's think of common titles for such worksheets.

Perhaps "AREA AND CIRCUMFERENCE".

But that's long.

Perhaps the answer is "CODED" because the first five letters are C,O,D,E,D — which is "CODED".

And the rest is for "TITLE", but "TITLE" is not part of the answer.

The question is "What Is the Title of This Picture?" — and the picture is the worksheet, so the title might be "CODED" as in the coded title section.

But that seems weak.

Let's look at the very beginning of the worksheet. It says "What Is the Title of This Picture?" and then "CODED TITLE" below, so perhaps the title is "CODED TITLE".

But that's circular.

Perhaps the title is "THE CIRCLE" or "CIRCLE PROBLEMS".

Let's calculate the average or something.

I recall that in some worksheets, the answer is "PI" because pi is involved.

But "PI" is 2 letters.

Perhaps "CIRCLE" is 6 letters.

Let's list the unique values: 18.84, 28.26, 31.4, 78.5, and 17.27, 28.27, 178.50 — but 28.27 is close to 28.26, so perhaps it's the same.

Perhaps for circle 1, if we use radius for area, etc.

Another thought: perhaps the "title" is formed by the first letter of the unit or something.

I think I need to accept that from the student's handwriting, they have spelled "CODED TITLE", but since that's the label, perhaps the actual title is "CODED" and the answer is "CODED".

But let's check the number of letters.

Perhaps the title is "FOUR" because there are four calculations.

But "FOUR" is 4 letters.

Let's count the letters in "CODED" — 5 letters.

In the coded title, the first 5 letters are C,O,D,E,D — which is "CODED".

Then the next 5 are T,I,T,L,E — "TITLE".

So perhaps the title is "CODED TITLE", and that's the answer.

But that seems odd for a homework problem.

Perhaps the title is "CIRCLES" and we need to see which letters are used.

Let's try to see if "CIRCLES" can be formed.

C - 18.84
I - ?
R - ?
C - 18.84 again?
L - 28.27?
E - 78.5
S - ?

Not matching.

Perhaps "AREA" or "CIRCUMFERENCE".

I think I found a better way.

Let's look at the instructions: "Use the diameter (d) or radius (r) of each circle to find the circumference (C) and area (A) of the circle."

Then "Write the answer in the coded title."

So for each circle, we have C and A, so for two circles, 4 values.

But the coded title has 10 blanks, so perhaps there are more circles, or perhaps for each, we do something else.

Perhaps "each circle" means we do for diameter and radius separately, but that doesn't make sense.

Another idea: perhaps the "title" is "PI" and we need to find pi, but pi is given as 3.14.

Perhaps the title is "3.14" but that's not a title.

Let's calculate the product or sum.

Sum of all areas: 28.26 + 78.5 = 106.76
Sum of circumferences: 18.84 + 31.4 = 50.24

Not nice.

Perhaps the title is "CIRCLE" and the letters are assigned based on the value.

I recall that in some worksheets, the answer is "THE CIRCLE" or "CIRCLES ARE GREAT".

Let's try "CIRCLES" : C,I,R,C,L,E,S

From our values:
C = 18.84
I = ?
R = ?
C = 18.84 again
L = 28.27?
E = 78.5
S = ?

Not sufficient.

Perhaps for circle 1, if we calculate the diameter from area or something.

From area 28.26, r^2 = 28.26/3.14 = 9, r=3, d=6, same as given.

I think I need to conclude that the title is "CODED" based on the first five letters.

But let's see the final answer expected.

Perhaps the title is "CODED TITLE" and that's it.

But let's look at the very top: "What Is the Title of This Picture?" and then the worksheet has "CODED TITLE" as a section, so perhaps the title of the picture is "CODED TITLE".

In that case, the answer is "CODED TITLE".

And the student has already filled it in.

So for the purpose of this problem, the title is "CODED TITLE".

But that seems too straightforward, and the calculations are for verification.

Perhaps the title is "CIRCLES" and we need to see.

Another idea: perhaps the "coded title" is to be read as the letters, and the title is the word, but in this case, it's "CODED TITLE", so the answer is "CODED TITLE".

I think I'll go with that.

So the title of the picture is "CODED TITLE".

But let's confirm with the calculations.

From circle 1: C=18.84 -> C, A=28.26 -> O
From circle 2: C=31.4 -> D, A=78.5 -> E
Then for the next D, perhaps it's the same as D, so 31.4 again.
Then T: perhaps from a different calculation, but in the image, they have 17.27 for T, which might be for a circle with diameter 5.5, but it's not given, so perhaps it's a mistake, or perhaps for circle 1, if we use radius for circumference: 2*3.14*3 = 18.84, same as before.

2*3.14*2.75 = 17.27, so radius 2.75, but not given.

Perhaps the worksheet has a third circle, but in the image, only two are visible.

Given that, and since the student has written "CODED TITLE", and the question is "What Is the Title of This Picture?", the answer is likely "CODED TITLE".

So I'll go with that.

Final Answer: CODED TITLE