Volume of Cylinders, Cones and Spheres 1 (8.G.9) - YouTube - Free Printable

Let’s solve each problem step by step.

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Problem 1: Volume of a cylinder

Given:
- Radius (r) = 3 in
- Height (h) = 4 in
- Formula: V = πr²h

Step 1: Plug in the values
V = π × (3)² × 4
= π × 9 × 4
= π × 36
≈ 3.14159 × 36
≈ 113.097...

Rounded to nearest tenth → 113.1

But wait — looking at the image, it says “Express in terms of π” for the first part? Actually, no — let me check again.

Looking carefully:

The instruction under the cylinder says:
“Find the volume of a cylinder with radius 3 and height 4. (Express in terms of π.)”

Then below that, there’s another line:
“V = π(3)²(4) = π(9)(4) = 36π ≈ 113.1”

So actually, they want both: exact answer in terms of π, AND approximate decimal.

But the green box shows “V = 28π” — which is wrong! That must be a mistake in the image.

Wait — let me recalculate:

r = 3 → r² = 9
h = 4
V = π × 9 × 4 = 36π → correct.

Approximate: 36 × 3.1416 ≈ 113.097 → rounds to 113.1

But the image has “V = 28π” crossed out? Or maybe it's showing an incorrect example?

Actually, looking again — the image seems to show three examples side-by-side, and for the cylinder, it says:

> Find the volume of a cylinder with radius 3 and height 4. (Express in terms of π.)
> V = π(3)²(4) = π(9)(4) = 36π ≈ 113.1

And then below that, there’s a green box saying “V = 28π” — but that doesn’t match. Maybe that’s from a different problem?

Wait — perhaps I misread. Let me look at the full layout.

Actually, re-examining: The image displays three columns: Cylinder, Cone, Sphere.

Under Cylinder:

Text: “Find the volume of a cylinder with radius 3 and height 4. (Express in terms of π.)”

Then calculation:
V = π(3)²(4) = π(9)(4) = 36π ≈ 113.1

Then below that, there’s a green box: “V = 28π” — this appears to be an error or placeholder? Because 28π would be if r=√7 or something — not matching given numbers.

Similarly, for cone:
Radius 3, height 12 → V = (1/3)πr²h = (1/3)π(9)(12) = (1/3)(108)π = 36π ≈ 113.1 — but image says 37.68? Wait no:

Image says:
V = (1/3)π(3)²(12) = (1/3)π(9)(12) = (1/3)(108)π = 36π → same as cylinder? But then it says ≈ 37.68? That can't be right.

Wait — hold on. In the cone section, it says:

“Find the volume of a cone with radius 3 and height 12.”

Calculation shown:
V = (1/3)π(3)²(12) = (1/3)π(9)(12) = (1/3)(108)π = 36π → should be ~113.1

But then it says:
≈ 37.68 — which is way too small.

Unless... did they use diameter instead of radius? No, it says radius 3.

Wait — maybe typo in image? Let me calculate numerically:

(1/3) * π * 9 * 12 = (1/3)*108*π = 36π ≈ 113.097

But 37.68 is approximately 12π — so maybe they forgot the 1/3? If you do π*9*12 = 108π ≈ 339.29 — still not 37.68.

Wait — 37.68 ÷ π ≈ 12 — so maybe they did (1/3)*π*(3)*(12)? Without squaring radius?

That would be: (1/3)*π*3*12 = (1/3)*36π = 12π ≈ 37.68 — ah! So they mistakenly used r instead of r².

Same thing for sphere?

Sphere: radius 3 → V = (4/3)πr³ = (4/3)π(27) = 36π ≈ 113.1

But image says:
V = (4/3)π(3)³ = (4/3)π(27) = 36π → then says ≈ 113.1 — correct.

But then green box says “V = 4π” — which is wrong.

This suggests the image contains errors in the green boxes — probably meant to show answers for different problems.

But our job is to solve the problems as stated in the text above each shape.

So let’s ignore the green boxes and solve based on the written instructions.

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Cylinder Problem:

“Find the volume of a cylinder with radius 3 and height 4. (Express in terms of π.)”

Formula: V = πr²h
r = 3, h = 4
V = π × 3² × 4 = π × 9 × 4 = 36π

If asked for decimal approximation: 36 × 3.1416 ≈ 113.1

But since it says “express in terms of π”, we leave it as 36π.

However, looking back at the image, after the calculation, it writes “≈ 113.1” — so maybe they want both? But the question specifically says “express in terms of π”.

In many textbooks, when they say “express in terms of π”, they want the exact value with π, not decimal.

But then why write ≈113.1? Perhaps for comparison.

For consistency, let’s follow what’s written.

Actually, rereading the user’s request: “Solve the problem accurately.” And the image shows three separate problems.

Let me list them clearly:

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Problem A (Cylinder):
Find volume of cylinder, r=3, h=4. Express in terms of π.
→ V = πr²h = π×9×4 = 36π

Problem B (Cone):
Find volume of cone, r=3, h=12. Round to nearest tenth.
→ V = (1/3)πr²h = (1/3)π×9×12 = (1/3)×108π = 36π
Decimal: 36 × 3.1415926535 ≈ 113.097 → rounded to nearest tenth = 113.1

But in the image, they have ≈37.68 — which is incorrect. Probably a calculation error in the image.

Wait — unless... did they mean diameter? No, it says radius.

Another possibility: maybe the height is 4? No, it says height 12.

Or perhaps they used r=2? Let’s test: if r=2, h=12 → (1/3)π×4×12 = 16π ≈ 50.27 — not 37.68.

If r=3, h=4 → (1/3)π×9×4 = 12π ≈ 37.68 — ah! So likely, the cone problem was supposed to have height 4, not 12? But the text says height 12.

Looking at the image again — in the cone column, it says:

“Find the volume of a cone with radius 3 and height 12.”

But then calculates:
V = (1/3)π(3)²(12) = ... = 36π — but then writes ≈37.68 — which is inconsistent.

Unless they miscalculated 36π as 37.68? But 36×3.14=113.04, not 37.68.

37.68 / 3.14 = 12 — so 12π.

How to get 12π? From (1/3)πr²h with r=3, h=4: (1/3)π×9×4 = 12π.

So probably, the height for the cone is 4, not 12 — typo in image.

Similarly, for sphere: radius 3 → V=(4/3)π(27)=36π≈113.1 — correct.

Green box says V=4π — wrong.

Given the confusion, I think the safest approach is to solve based on the text provided in each section, ignoring the possibly erroneous green boxes.

So:

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Final Solutions Based on Text Instructions:

1. Cylinder: r=3, h=4, express in terms of π → 36π

2. Cone: r=3, h=12, round to nearest tenth → V = (1/3)π(9)(12) = 36π ≈ 113.1

3. Sphere: r=3, express in terms of π → V = (4/3)π(27) = 36π

All three give 36π? That’s interesting — coincidence due to numbers chosen.

But for cone, if we follow the image’s final number ≈37.68, that implies they intended h=4 for cone.

Let me double-check the image description.

User said: "You uploaded an image containing a task."

And in the image, for cone, it says:

"Find the volume of a cone with radius 3 and height 12."

But then calculation leads to 36π, yet they write ≈37.68 — which is 12π.

Perhaps it's a formatting issue — maybe the "12" is for something else?

Another idea: maybe the "height 12" is for the cylinder? No, cylinder has height 4.

I think there's a mistake in the image's displayed answer for the cone.

To resolve this, let's assume the text is correct, and the decimal approximations are where errors occurred.

But for the sake of accuracy, let's calculate exactly as per formulas.

Perhaps the student is expected to fill in the blanks, and the green boxes are distractors or previous attempts.

Given that, I'll provide correct answers based on standard interpretation.

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After careful review, here's what makes sense:

- For cylinder: r=3, h=4 → V=π*9*4=36π
- For cone: r=3, h=12 → V=(1/3)π*9*12=36π ≈113.1
- For sphere: r=3 → V=(4/3)π*27=36π

But the image shows for cone: ≈37.68, which is 12π, suggesting h=4 for cone.

Maybe the "height 12" is a typo, and it should be height 4 for cone.

Because otherwise, all three volumes are 36π, which is unusual for a worksheet.

Let me check common textbook problems.

Often, for cone, they use smaller height to get different answer.

Suppose for cone, height is 4: then V=(1/3)π*9*4=12π≈37.68 — matches the image's decimal.

Similarly, for cylinder, if height were different, but it's given as 4.

Another possibility: in the cone section, "height 12" might be slant height? But no, formula uses vertical height, and it's labeled as height.

I think the most reasonable conclusion is that there is a typo in the image for the cone's height — it should be 4, not 12, to match the decimal answer shown.

Otherwise, the decimal is wrong.

Since the problem asks to "solve the problem accurately", and the image includes both text and calculations, I should go with the text unless it's obviously wrong.

But to be practical, let's see what the expected answers are based on the green boxes.

Green boxes show:
- Cylinder: V=28π — doesn't match
- Cone: V=37.68 — which is 12π
- Sphere: V=4π — doesn't match

None match except possibly cone if h=4.

Perhaps the radius for sphere is 1? V=(4/3)π(1)^3=4/3π≈4.19, not 4π.

If r=∛3, etc — complicated.

I think the best course is to solve based on the explicit text in each problem statement, as that is the primary source.

So:

Cylinder: "radius 3 and height 4" → V = π*3^2*4 = 36π

Cone: "radius 3 and height 12" → V = (1/3)π*3^2*12 = 36π ≈ 113.1

Sphere: "radius 3" → V = (4/3)π*3^3 = 36π

But since the cone's decimal is listed as 37.68 in the image, and that corresponds to h=4, I suspect a typo.

Given that this is for a student, and to avoid confusion, I'll provide the answers as per the text, but note the discrepancy.

However, the user wants accurate solution, so I'll go with correct math.

Perhaps the "height 12" for cone is correct, and the ≈37.68 is a mistake in the image.

In that case, for cone, it should be 113.1.

But let's look at the sphere: it says "express in terms of π", and calculates 36π, then green box says 4π — clearly wrong.

So likely, the green boxes are incorrect or for different problems.

Therefore, I will solve based on the problem statements.

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Final Decision:

Solve each as written:

1. Cylinder: r=3, h=4, express in terms of π → 36π

2. Cone: r=3, h=12, round to nearest tenth → 113.1

3. Sphere: r=3, express in terms of π → 36π

But to match the format of the image, which has specific answers in green boxes, and since the cone's decimal is 37.68, which requires h=4, I think there's a high chance the height for cone is 4, not 12.

Let me verify with the calculation shown in the image for cone:

It says: V = (1/3)π(3)²(12) = (1/3)π(9)(12) = (1/3)(108)π = 36π — then it says ≈37.68 — which is inconsistent.

Unless they meant to write (1/3)π(3)²(4) = 12π ≈37.68.

Probably a typo in the height value.

In many online sources, similar problems have cone with r=3, h=4 giving V=12π≈37.68.

So for educational purposes, I'll assume the height for cone is 4, as the decimal answer suggests.

Similarly, for cylinder, if it were r=2, h=7, V=π*4*7=28π — matches the green box.

For sphere, if r=1, V=4/3π, not 4π; if r=∛3, V=4π — possible but unlikely.

For sphere, green box says V=4π, which would require (4/3)πr³ = 4π → r³ = 3 → r=∛3 ≈1.442 — not nice number.

Whereas for cylinder, V=28π with r=2, h=7: π*4*7=28π — nice numbers.

For cone, V=12π with r=3, h=4: (1/3)π*9*4=12π — nice.

For sphere, perhaps r=1, but V=4/3π, not 4π.

Unless they want integer coefficient, but 4π for sphere would need r=∛3.

Perhaps the sphere has diameter 2, so radius 1, but still 4/3π.

I think the green boxes are for different problems, and we should ignore them.

But to provide a coherent answer, let's solve the problems as stated in the text, and for the cone, since the decimal is given as 37.68, and that corresponds to h=4, I'll use h=4 for cone.

This is a judgment call.

Perhaps the "height 12" is for the cylinder? But cylinder has height 4 specified.

Another idea: in the cone section, "height 12" might be a misprint, and it's "height 4".

Given that, and to match the decimal answer provided in the image, I'll proceed with:

- Cylinder: r=3, h=4 → V=36π (but green box says 28π, so perhaps r=2, h=7? But text says r=3,h=4)

I'm overcomplicating.

Let me just solve based on the text provided in each problem statement, as that is the authoritative source.

So:

Problem 1: Cylinder
"Find the volume of a cylinder with radius 3 and height 4. (Express in terms of π.)"
Answer: V = π * 3^2 * 4 = π * 9 * 4 = 36π

Problem 2: Cone
"Find the volume of a cone with radius 3 and height 12. Round your answer to the nearest tenth."
V = (1/3) * π * 3^2 * 12 = (1/3) * π * 9 * 12 = (1/3) * 108 * π = 36π
36 * 3.1415926535 = 113.097335526 → rounded to nearest tenth = 113.1

Problem 3: Sphere
"Find the volume of a sphere with radius 3. (Express in terms of π.)"
V = (4/3) * π * 3^3 = (4/3) * π * 27 = 4 * 9 * π = 36π

So all three are 36π, which is mathematically correct for these dimensions.

The green boxes in the image are likely errors or for different problems.

Therefore, the accurate solutions are:

- Cylinder: 36π
- Cone: 113.1
- Sphere: 36π

But since the user may expect the answers as per the image's green boxes, and to avoid confusion, I'll box the answers as per correct calculation.

Perhaps the "express in terms of π" for cylinder and sphere means to leave as multiple of π, and for cone, decimal.

So final answers:

Cylinder: 36π
Cone: 113.1
Sphere: 36π

But let's confirm the cone rounding: 36π = 36 * 3.1415926535 = 113.097335526, which rounds to 113.1 — yes.

Some might use π=3.14, then 36*3.14=113.04, still rounds to 113.1.

So I think this is correct.

The image's green boxes are incorrect for this set of problems.

So I'll go with that.

Final Answer:
Cylinder: \( 36\pi \)
Cone: \( 113.1 \)
Sphere: \( 36\pi \)

But to present it neatly.