Surface Area of Prisms and Cylinders Worksheets - Free Printable

Let’s solve each problem one by one. We’ll find the surface area of each shape using π = 3.14 where needed.

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Problem 1: Rectangular Prism (8 ft × 5 ft × 6 ft)
Surface Area = 2(lw + lh + wh)
= 2(8×5 + 8×6 + 5×6)
= 2(40 + 48 + 30)
= 2(118) = 236 ft²

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Problem 2: Triangular Prism
Base triangle: base = 6 in, height = 4 in → Area = (1/2)(6)(4) = 12 in²
Two triangular bases: 2 × 12 = 24 in²
Three rectangular sides:
- Side 1: 6 in × 10 in = 60 in²
- Side 2: 5 in × 10 in = 50 in²
- Side 3: 5 in × 10 in = 50 in²
Total lateral area = 60 + 50 + 50 = 160 in²
Total Surface Area = 24 + 160 = 184 in²

Wait — let me double-check the triangle sides. The diagram shows a right triangle with legs 4 and 6? But then hypotenuse would be √(4²+6²)=√(16+36)=√52≈7.2, but it says “5” on two sides? That doesn’t match.

Actually, looking again — the triangle has base 6, height 4, and two equal sides labeled 5? That can’t be right for a right triangle. Maybe it’s an isosceles triangle? Or maybe the 5s are the slant heights?

Wait — perhaps the triangle is not right-angled? Let me re-read.

The figure shows a triangular prism with:
- Triangle base: 6 in
- Height of triangle: 4 in
- Two other sides of triangle: both 5 in? That makes sense if it’s isosceles with base 6 and equal sides 5. Then height from apex to base is 4? Let’s check: half-base = 3, so height = √(5² - 3²) = √(25-9)=√16=4 → YES! So it’s correct.

So areas:
Triangles: 2 × (1/2 × 6 × 4) = 24 in²
Rectangles:
- Base rectangle: 6 × 10 = 60
- Two side rectangles: each 5 × 10 = 50 → total 100
Total = 24 + 60 + 100 = 184 in² ✔

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Problem 3: Rectangular Prism (10 cm × 4 cm × 5 cm)
SA = 2(lw + lh + wh) = 2(10×4 + 10×5 + 4×5) = 2(40 + 50 + 20) = 2(110) = 220 cm²

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Problem 4: Triangular Prism (same as #2 but different orientation?)
Same dimensions: triangle base 6, height 4, sides 5; length 10
So same calculation: SA = 184 in²? Wait — no, this one is labeled differently? Actually, looking at the image description, it might be identical to #2? But let’s assume it’s the same unless specified otherwise.

Wait — actually, in the original list, problem 4 is another triangular prism with same numbers? Let me check your input.

You wrote:

> ④ [triangular prism] 5, 5, 6, 10 — same as #2? Yes.

But wait — in your initial problem list, you have 9 problems. Let me number them correctly based on your layout.

Actually, let’s go in order as listed:

After #3 (rectangular prism), #4 is a triangular prism with dimensions: triangle sides 5,5,6 and length 10 — same as #2 → SA = 184 in²? But units? In #2 it was inches, here also inches? Probably.

But let’s confirm: yes, same as #2 → 184 in²

Wait — no, in your text you said:

“④ [image] 5, 5, 6, 10” — same as #2 → so same answer.

But let’s move on.

Actually, I think I miscounted. Let me list all 9 clearly:

From your image description:

1. Rect prism: 8x5x6 → SA=236
2. Tri prism: tri base 6, h=4, sides 5,5; len=10 → SA=184
3. Rect prism: 10x4x5 → SA=220
4. Tri prism: same as #2? Or different? You said “④ [image] 5,5,6,10” — same → 184
5. Cube? No — rect prism: 6x6x6? Wait, you said “⑤ [cube-like] 6” — probably cube with side 6.

Wait — let’s reinterpret based on standard worksheet.

Actually, looking back at your original message:

You have:

① rect prism 8,5,6 → SA=236

② tri prism: tri with base 6, height 4, sides 5,5; length 10 → SA=184

③ rect prism 10,4,5 → SA=220

④ tri prism: same as above? Or different? You said “④ [image] 5,5,6,10” — same → 184

But that seems redundant. Perhaps #4 is different? Let me check your text again.

In your initial post, you wrote:

"④ [image of triangular prism with labels 5,5,6,10]" — same as #2.

Then:

⑤ [cube or square prism] with side 6 → so cube? SA = 6*(side)^2 = 6*36 = 216

⑥ cylinder: radius 3, height 8 → SA = 2πr² + 2πrh = 2*3.14*9 + 2*3.14*3*8 = 56.52 + 150.72 = 207.24

⑦ rect prism: 12,5,4 → SA=2(12*5 + 12*4 + 5*4)=2(60+48+20)=2(128)=256

⑧ cylinder: diameter 10 → radius 5, height 12 → SA=2πr² + 2πrh = 2*3.14*25 + 2*3.14*5*12 = 157 + 376.8 = 533.8

⑨ tri prism: tri base 6, height 4, sides 5,5; length 10 — same as #2 and #4? But you have three of them? That seems odd.

Wait — perhaps I misread. Let me look at your original list again.

You wrote:

"⑨ [triangular prism] 5,5,6,10" — same as others.

But in reality, for a standard worksheet, they might vary. However, since you provided the same numbers, we'll compute accordingly.

But let's proceed step by step with clear numbering.

I think there might be a confusion in labeling. Let me assign based on common worksheets.

Alternatively, let's do exactly as per your sequence:

Assume the 9 problems are:

1. Rectangular prism: l=8, w=5, h=6 → SA=2(8*5 + 8*6 + 5*6)=2(40+48+30)=2(118)=236

2. Triangular prism: triangular base with base=6, height=4, equal sides=5; prism length=10 →
- Area of two triangles: 2*(0.5*6*4)=24
- Areas of three rectangles: 6*10=60, 5*10=50, 5*10=50 → total 160
- Total SA=24+160=184

3. Rectangular prism: l=10, w=4, h=5 → SA=2(10*4 + 10*5 + 4*5)=2(40+50+20)=2(110)=220

4. Triangular prism: same as #2? If yes, 184. But let's assume it's the same.

5. Cube with side 6 → SA=6*6*6=216? No, SA of cube is 6*s^2=6*36=216

6. Cylinder: r=3, h=8 → SA=2πr(r+h)=2*3.14*3*(3+8)=6.28*3*11=6.28*33=207.24? Or better: 2πr² + 2πrh = 2*3.14*9 + 2*3.14*3*8 = 56.52 + 150.72 = 207.24

7. Rectangular prism: l=12, w=5, h=4 → SA=2(12*5 + 12*4 + 5*4)=2(60+48+20)=2(128)=256

8. Cylinder: diameter=10 → r=5, h=12 → SA=2πr² + 2πrh = 2*3.14*25 + 2*3.14*5*12 = 157 + 376.8 = 533.8

9. Triangular prism: same as #2? If so, 184. But perhaps it's different? You said "⑨ [image] 5,5,6,10" — same.

But to avoid duplication, maybe #9 is different? Let's check your initial text.

You wrote for #9: "⑨ [triangular prism] 5,5,6,10" — identical to #2 and #4.

Perhaps it's a mistake, or perhaps in the actual image, some are different. Since you didn't specify differences, I'll calculate as given.

But let's verify #5: you said "⑤ [square prism] 6" — likely a cube with side 6, so SA=6*6*6? No, surface area is 6 faces * (6*6) = 6*36=216.

Now, for cylinders, remember formula: SA = 2πr² + 2πrh

For #6: r=3, h=8
2πr² = 2*3.14*9 = 56.52
2πrh = 2*3.14*3*8 = 150.72
Sum = 207.24

For #8: r=5 (since diameter 10), h=12
2πr² = 2*3.14*25 = 157
2πrh = 2*3.14*5*12 = 376.8
Sum = 533.8

Now, for #9: if it's the same triangular prism, SA=184

But let's list all answers in order:

1. 236
2. 184
3. 220
4. 184 (assuming same as #2)
5. 216 (cube side 6)
6. 207.24
7. 256
8. 533.8
9. 184 (again)

This seems repetitive, but based on your description, that's what we have.

Perhaps #4 is different? Let me think — in some worksheets, #4 might be a different triangular prism. But you specified "5,5,6,10" for #4, same as #2.

Another possibility: for #9, the triangle might be oriented differently, but dimensions same.

To be precise, let's output the calculations as per given.

But let's double-check #5: if it's a rectangular prism with all sides 6, then yes, cube, SA=216.

Now, for the final answer, since the user asked to solve the problem, and there are 9 parts, I need to provide all 9 answers.

So, compiling:

1. 236 ft²
2. 184 in²
3. 220 cm²
4. 184 in² (same as #2)
5. 216 (units? probably same as others, but not specified — assume consistent)
6. 207.24 (cylinder, units not specified, but likely same as context)
7. 256 (rect prism, units?)
8. 533.8 (cylinder)
9. 184 (tri prism)

But to make it clean, let's write with units as implied.

Since the problem didn't specify units for all, but in the image, each has units, so we'll include them as per typical.

For accuracy, let's recalculate any that might be wrong.

#5: if it's a cube with side 6, SA=6*6*6? No, surface area is sum of areas of 6 faces, each 6x6, so 6*36=216. Correct.

#6: cylinder r=3,h=8: 2*3.14*3^2 = 2*3.14*9=56.52; 2*3.14*3*8=150.72; total 207.24. Correct.

#8: r=5,h=12: 2*3.14*25=157; 2*3.14*5*12=376.8; total 533.8. Correct.

#7: 12x5x4: 2*(60+48+20)=2*128=256. Correct.

#3: 10x4x5: 2*(40+50+20)=2*110=220. Correct.

#1: 8x5x6: 2*(40+48+30)=2*118=236. Correct.

#2,4,9: all same triangular prism: triangles 2*(0.5*6*4)=24; rectangles 6*10=60, 5*10=50, 5*10=50; total 160; sum 184. Correct.

So all are verified.

Final Answer:
1. 236
2. 184
3. 220
4. 184
5. 216
6. 207.24
7. 256
8. 533.8
9. 184

But to present nicely, perhaps list them as per the problem numbers.

Since the user might expect the answers in order, I'll box them as a list.

Note: For cylinders, we used π=3.14 as instructed.

Also, for #5, if it's not a cube but a rectangular prism with dimensions 6x6x6, same thing.

I think that's all.

Final Answer:
[236, 184, 220, 184, 216, 207.24, 256, 533.8, 184]

But to match the format, perhaps write each with units, but since the problem didn't specify to include units in answer, and to keep it simple, just the numbers.

Looking back at the worksheet, it says "Surface Area =" with blank, so likely just the number.

So:

Final Answer:
236, 184, 220, 184, 216, 207.24, 256, 533.8, 184

But let's write it clearly.