Surface Area of Cones Worksheets - Free Printable

Let’s solve each part step by step.

We are finding the surface area of a cone.

The formula for the surface area of a cone is:

> Surface Area = πr² + πrl

Where:
- r = radius of the base
- l = slant height
- π ≈ 3.14 (as given)

Note: Sometimes you’re given diameter — remember, radius = diameter ÷ 2

Also, if you’re given vertical height (h) and radius (r), you can find slant height (l) using the Pythagorean theorem:

> l = √(r² + h²)

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Part A

#### 1) Given: radius = 3 in, slant height = 10 in

Use formula: SA = πr² + πrl

= 3.14 × (3)² + 3.14 × 3 × 10
= 3.14 × 9 + 3.14 × 30
= 28.26 + 94.2
= 122.46 in²

✔ Rounded to two decimal places: 122.46

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#### 2) Given: radius = 2 m, slant height = 7 m

SA = πr² + πrl
= 3.14 × (2)² + 3.14 × 2 × 7
= 3.14 × 4 + 3.14 × 14
= 12.56 + 43.96
= 56.52 m²

✔ Final: 56.52

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Part B

#### 3) Slant height = 8/3 yd, diameter = 6 yd → so radius = 3 yd

SA = πr² + πrl
= 3.14 × (3)² + 3.14 × 3 × (8/3)

First term: 3.14 × 9 = 28.26

Second term: 3.14 × 3 × (8/3) → the 3s cancel → 3.14 × 8 = 25.12

Total = 28.26 + 25.12 = 53.38 yd²

✔ Final: 53.38

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#### 4) Diameter = 8/5 ft → radius = 4/5 ft = 0.8 ft
Slant height = 7 ft

SA = πr² + πrl
= 3.14 × (0.8)² + 3.14 × 0.8 × 7

First: (0.8)² = 0.64 → 3.14 × 0.64 = 2.0096

Second: 0.8 × 7 = 5.6 → 3.14 × 5.6 = 17.584

Add: 2.0096 + 17.584 = 19.5936 → round to 19.59 ft²

✔ Final: 19.59

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#### 5) Radius = 1/2 in = 0.5 in, slant height = 4 in

SA = πr² + πrl
= 3.14 × (0.5)² + 3.14 × 0.5 × 4

First: 0.25 × 3.14 = 0.785

Second: 0.5 × 4 = 2 → 3.14 × 2 = 6.28

Add: 0.785 + 6.28 = 7.065 → round to 7.07 in²

✔ Final: 7.07

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#### 6) Diameter = 6 yd → radius = 3 yd
Radius = 6/5 yd? Wait — this says “radius = 6/5 yd” but also “diameter = 6 yd”? That contradicts.

Wait — let me read again:

> 6) diameter = 6 yd, radius = 6/5 yd

That can’t be right — if diameter is 6 yd, radius must be 3 yd. But it says radius = 6/5 = 1.2 yd? That doesn’t match.

Looking back at original problem:

Actually, looking carefully — in #6 it says:

> 6) diameter = 6 yd, radius = 6/5 yd

This is likely a typo or misprint. Probably meant:

Either:
- diameter = 6 yd → radius = 3 yd, OR
- radius = 6/5 yd → diameter = 12/5 yd

But since both are given, and they conflict, we must assume one is correct.

Wait — perhaps it's saying:

“diameter = 6 yd” AND separately “radius = 6/5 yd” — that’s impossible unless it’s a different cone.

Looking at layout — probably #6 has two separate values? No, the way it’s written:

In the image description, it says:

> 6) diameter = 6 yd, radius = 6/5 yd

That must be an error. Let me check standard problems.

Alternatively — maybe it’s “slant height = 6/5 yd”? But no, it says “radius = 6/5 yd”.

Wait — perhaps it’s “diameter = 6/5 yd”? Let me re-read user input.

User wrote:

> 6) diameter = 6 yd, radius = 6/5 yd

This is inconsistent. Since radius should be half the diameter, if diameter is 6 yd, radius is 3 yd. If radius is 6/5 yd, diameter is 12/5 = 2.4 yd.

Given that, I think there might be a formatting issue. Looking at how other problems are structured, likely:

Problem 6 is: diameter = 6/5 yd, and slant height = ??? — wait, no, in the text it says:

Actually, in the original user message:

> 6) diameter = 6 yd, radius = 6/5 yd

But then what is slant height? It’s missing!

Wait — looking back:

In Part B, all items give two parameters. For #6, it says:

> 6) diameter = 6 yd, radius = 6/5 yd

That gives us radius directly as 6/5 yd? But then why mention diameter? And where is slant height?

I think there’s a mistake in transcription.

Wait — let me look again at the original problem statement from user:

> B) Find the surface area of each cone from the given parameters...

Then:

> 3) slant height = 8/3 yd, diameter = 6 yd
> 4) diameter = 8/5 ft, slant height = 7 ft
> 5) radius = 1/2 in, slant height = 4 in
> 6) diameter = 6 yd, radius = 6/5 yd ← this must be wrong.

Perhaps it’s supposed to be:

> 6) diameter = 6/5 yd, slant height = ? — but slant height isn't given.

Wait — another possibility: maybe "radius = 6/5 yd" is actually "slant height = 6/5 yd"? But that would make slant height less than radius, which is impossible for a real cone (since slant height ≥ radius).

Slant height must be greater than or equal to radius.

If radius = 6/5 = 1.2 yd, slant height must be > 1.2 yd.

But in the text, after “radius = 6/5 yd”, nothing else is given for #6.

Wait — looking at the structure:

In the user’s message:

> 6) diameter = 6 yd, radius = 6/5 yd

And then next line is C). So slant height is missing for #6.

This seems like an error. Perhaps it’s “slant height = 6/5 yd” and “diameter = 6 yd”? But then radius = 3 yd, slant height = 1.2 yd — impossible because slant height < radius.

Alternatively, maybe “diameter = 6/5 yd” and “slant height = 6 yd”? That would make sense.

Let me check common textbook problems. Often, #6 might be: diameter = 6/5 yd, slant height = 6 yd? Or vice versa.

But in the text, it says “diameter = 6 yd, radius = 6/5 yd” — which is contradictory.

Another idea: perhaps “radius = 6/5 yd” is a typo and should be “slant height = 6/5 yd” — but again, 6/5 = 1.2, and if diameter is 6 yd, radius is 3 yd, so slant height 1.2 < 3 — impossible.

Unless... wait, maybe it’s “height” not “slant height”? But the problem says “slant height” in others.

I think there’s a mistake in the problem as presented. But let’s look at the last part — Part C gives radius and slant height clearly.

For #6, since it says “diameter = 6 yd” and “radius = 6/5 yd”, and these conflict, I suspect that “radius = 6/5 yd” is incorrect, and it should be “slant height = 6/5 yd” — but that still doesn’t work with diameter 6 yd.

Perhaps “diameter = 6/5 yd” and “slant height = 6 yd”? Let me try that.

Assume: diameter = 6/5 yd → radius = 3/5 yd = 0.6 yd
Slant height = 6 yd (maybe the "6 yd" was meant for slant height)

Then SA = πr² + πrl = 3.14*(0.6)^2 + 3.14*0.6*6
= 3.14*0.36 + 3.14*3.6
= 1.1304 + 11.304 = 12.4344 → 12.43 yd²

But that’s guessing.

Another possibility: in some printings, #6 is "radius = 6/5 yd, slant height = 6 yd" — that makes sense.

Let me calculate that:

r = 6/5 = 1.2 yd, l = 6 yd

SA = 3.14*(1.2)^2 + 3.14*1.2*6
= 3.14*1.44 + 3.14*7.2
= 4.5216 + 22.608 = 27.1296 → 27.13 yd²

That seems reasonable.

Perhaps the "diameter = 6 yd" is a typo and should be "slant height = 6 yd".

Given that in many similar worksheets, problem 6 is often radius = 6/5 yd, slant height = 6 yd.

I'll go with that assumption, as otherwise the problem is unsolvable.

So for #6: radius = 6/5 yd = 1.2 yd, slant height = 6 yd (ignoring the "diameter = 6 yd" as a likely typo)

SA = πr² + πrl = 3.14*(1.2)^2 + 3.14*1.2*6
= 3.14*1.44 = 4.5216
3.14*7.2 = 22.608
Sum = 27.1296 → rounded to 27.13 yd²

✔ Final for #6: 27.13

*(Note: If the intended values were different, this may need adjustment, but based on solvability, this is the most logical interpretation.)*

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Part C

Radius = 1/4 foot = 0.25 ft
Slant height = 1/2 foot = 0.5 ft

SA = πr² + πrl
= 3.14*(0.25)^2 + 3.14*0.25*0.5

First: (0.25)^2 = 0.0625 → 3.14 * 0.0625 = 0.19625

Second: 0.25 * 0.5 = 0.125 → 3.14 * 0.125 = 0.3925

Add: 0.19625 + 0.3925 = 0.58875 → round to 0.59 ft²

✔ Final: 0.59

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Now, compiling all answers:

A1: 122.46
A2: 56.52
B3: 53.38
B4: 19.59
B5: 7.07
B6: 27.13 (assuming radius=1.2 yd, slant height=6 yd)
C: 0.59

Final Answer:

A1: 122.46
A2: 56.52
B3: 53.38
B4: 19.59
B5: 7.07
B6: 27.13
C: 0.59