Volume of Prisms and Cylinders worksheet - Free Printable

Let’s solve each problem one by one. We’ll use the formula for volume:

- For prisms (including rectangular prisms and triangular prisms):
→ Volume = Base Area × Height

- For cylinders:
→ Volume = π × r² × h
(We’re told to use 3.14 for π)

We’ll round each answer to the nearest tenth.

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Problem 1: Triangular Prism

Base is a right triangle with legs 22 in. and 22 in.
Area of base = (1/2) × 22 × 22 = 242 in²
Height of prism = 42 in.
Volume = 242 × 42 = 10,164 in³
→ Already whole number → 10,164.0 in³

Wait — let me double-check:
(1/2)*22*22 = 242 ✔️
242 * 42:
242 * 40 = 9,680
242 * 2 = 484
Total = 9,680 + 484 = 10,164 ✔️
So, 10,164.0

But wait — looking at the diagram again, maybe the 42 in. is the length along the prism? Yes, that’s correct. So yes, 10,164.0

Actually, let me check if I misread the dimensions. The triangle has two sides labeled 22 in., and the prism extends 42 in. So yes, correct.

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Problem 2: Cylinder

Radius = 6.5 cm, height = 16 cm
Volume = 3.14 × (6.5)² × 16
First, 6.5² = 42.25
Then, 3.14 × 42.25 = let’s calculate:
3 × 42.25 = 126.75
0.14 × 42.25 = 5.915
Total = 126.75 + 5.915 = 132.665
Now multiply by 16:
132.665 × 16
= 132.665 × 10 = 1,326.65
+ 132.665 × 6 = 795.99
Total = 1,326.65 + 795.99 = 2,122.64
Round to nearest tenth → 2,122.6 cm³

Wait — let me recalculate more carefully:

3.14 × 42.25 = ?

Do 314 × 4225 / 10000 (since 3.14 = 314/100, 42.25 = 4225/100)

Easier:
3.14 × 42.25
Break it:
3 × 42.25 = 126.75
0.14 × 42.25 = (0.1 × 42.25) + (0.04 × 42.25) = 4.225 + 1.69 = 5.915
Sum: 126.75 + 5.915 = 132.665 ✔️

Now 132.665 × 16:

132.665 × 10 = 1,326.65
132.665 × 6 = 795.99
Add: 1,326.65 + 795.99 = 2,122.64 → rounds to 2,122.6

Yes.

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Problem 3: Cube

All sides 13 m
Volume = side³ = 13 × 13 × 13
13×13 = 169
169×13:
170×13 = 2,210 minus 1×13 = 13 → 2,210 - 13 = 2,197
So 2,197.0 m³

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Problem 4: Rectangular Prism

Dimensions: 45 cm × 12 cm × 6 cm
Volume = 45 × 12 × 6
First, 45 × 12 = 540
Then 540 × 6 = 3,240
→ 3,240.0 cm³

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Problem 5: Triangular Prism

Base is triangle with base 28 m, height 18 m? Wait — look at diagram.

It shows a triangular prism where the triangular face has base 28 m and height 18 m? But then the length of the prism is 10 m?

Wait — actually, in the diagram, the triangle has base 28 m and height 18 m, and the prism extends 10 m perpendicular to that triangle.

So area of triangular base = (1/2) × 28 × 18 = 14 × 18 = 252 m²
Volume = 252 × 10 = 2,520 m³
→ 2,520.0 m³

Wait — but let me confirm orientation. Sometimes the “height” of the prism might be different. But here, since it's drawn as a triangular prism with the triangle on the end, and 10 m is the length, yes.

Alternatively, if the 10 m was the height of the triangle, but no — the diagram labels 28 m and 18 m on the triangle, and 10 m as the depth. So yes.

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Problem 6: Cylinder (lying on its side)

Diameter = 32 cm → radius = 16 cm
Length (height of cylinder) = 15 cm
Volume = π × r² × h = 3.14 × (16)² × 15
16² = 256
3.14 × 256 = ?
3 × 256 = 768
0.14 × 256 = 35.84
Total = 768 + 35.84 = 803.84
Now × 15:
803.84 × 10 = 8,038.4
803.84 × 5 = 4,019.2
Total = 8,038.4 + 4,019.2 = 12,057.6
→ 12,057.6 cm³

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Problem 7: Rectangular Prism

Dimensions: 11 in. × 17 in. × 31 in.
Volume = 11 × 17 × 31
First, 11 × 17 = 187
Then 187 × 31
= 187 × 30 + 187 × 1 = 5,610 + 187 = 5,797
→ 5,797.0 in³

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Problem 8: Triangular Prism

Triangle base: legs 14 m and 14 m (right triangle?)
Area = (1/2) × 14 × 14 = 98 m²
Prism length = 27 m
Volume = 98 × 27
Calculate: 100×27 = 2,700 minus 2×27=54 → 2,700 - 54 = 2,646
→ 2,646.0 m³

Wait — is it a right triangle? Diagram shows two sides 14 m meeting at right angle? It looks like it, since it's drawn with a square corner. So yes.

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Problem 9: Cube

Side = 14.3 ft
Volume = (14.3)^3
First, 14.3 × 14.3
14 × 14 = 196
14 × 0.3 = 4.2
0.3 × 14 = 4.2
0.3 × 0.3 = 0.09
Better: (14 + 0.3)^2 = 14^2 + 2×14×0.3 + 0.3^2 = 196 + 8.4 + 0.09 = 204.49
Now multiply by 14.3:
204.49 × 14.3
Break into: 204.49 × 14 + 204.49 × 0.3

First, 204.49 × 10 = 2,044.9
204.49 × 4 = 817.96
So 2,044.9 + 817.96 = 2,862.86

Then 204.49 × 0.3 = 61.347

Total = 2,862.86 + 61.347 = 2,924.207

Round to nearest tenth → 2,924.2 ft³

Let me verify:

14.3³ = ?

Use calculator-style:

14.3 × 14.3 = 204.49 ✔️

204.49 × 14.3:

Do 20449 × 143 / 1000 (since 204.49 = 20449/100, 14.3=143/10 → total denominator 1000)

20449 × 143:

First, 20449 × 100 = 2,044,900
20449 × 40 = 817,960
20449 × 3 = 61,347
Sum: 2,044,900 + 817,960 = 2,862,860 + 61,347 = 2,924,207

Divide by 1000 → 2,924.207 → rounds to 2,924.2

Yes.

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Now, compiling all answers:

1. 10,164.0 in³
2. 2,122.6 cm³
3. 2,197.0 m³
4. 3,240.0 cm³
5. 2,520.0 m³
6. 12,057.6 cm³
7. 5,797.0 in³
8. 2,646.0 m³
9. 2,924.2 ft³

I think that’s all. Let me just quickly recheck any that might have been tricky.

Problem 1: triangular prism — base area (1/2)*22*22=242, times 42=10,164 ✔️
Problem 2: cylinder — 3.14*(6.5)^2*16=3.14*42.25*16=132.665*16=2,122.64→2,122.6 ✔️
Problem 5: triangular prism — (1/2)*28*18=252, times 10=2,520 ✔️
Problem 6: cylinder — radius 16, so 3.14*256*15=803.84*15=12,057.6 ✔️
Problem 9: cube 14.3^3=2,924.207→2,924.2 ✔️

All good.

Final Answer:
1. 10164.0
2. 2122.6
3. 2197.0
4. 3240.0
5. 2520.0
6. 12057.6
7. 5797.0
8. 2646.0
9. 2924.2