Volume of a Pyramid - MathVine.com - Free Printable

Let’s solve each pyramid volume problem step by step.

The formula for the volume of a pyramid is:

Volume = (1/3) × Base Area × Height

For all these pyramids, the base is a rectangle (or square), so:

Base Area = length × width

Then multiply that by the height and divide by 3.

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Problem 1:
- Base: 9.8 ft × 10.4 ft
- Height: 12.6 ft

Step 1: Base area = 9.8 × 10.4
→ 9.8 × 10 = 98
→ 9.8 × 0.4 = 3.92
→ Total = 98 + 3.92 = 101.92 ft²

Step 2: Volume = (1/3) × 101.92 × 12.6
First, 101.92 × 12.6
Break it down:
101.92 × 10 = 1019.2
101.92 × 2 = 203.84
101.92 × 0.6 = 61.152
Add them: 1019.2 + 203.84 = 1223.04; +61.152 = 1284.192

Now divide by 3:
1284.192 ÷ 3 = 428.064 ft³

✔ Final Answer for #1: 428.064

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Problem 2:
- Base: 11 m × 14.2 m
- Height: 15.3 m

Step 1: Base area = 11 × 14.2
= 11 × 14 = 154; 11 × 0.2 = 2.2 → total = 156.2 m²

Step 2: Volume = (1/3) × 156.2 × 15.3
First, 156.2 × 15.3
Break it:
156.2 × 15 = 2343
156.2 × 0.3 = 46.86
Total = 2343 + 46.86 = 2389.86

Divide by 3:
2389.86 ÷ 3 = 796.62 m³

✔ Final Answer for #2: 796.62

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Problem 3:
- Base: 16.3 cm × 12.8 cm
- Height: 19.2 cm

Step 1: Base area = 16.3 × 12.8
Calculate:
16 × 12.8 = 204.8
0.3 × 12.8 = 3.84
Total = 204.8 + 3.84 = 208.64 cm²

Step 2: Volume = (1/3) × 208.64 × 19.2
First, 208.64 × 19.2
Break it:
208.64 × 20 = 4172.8
Minus 208.64 × 0.8 = 166.912
So: 4172.8 - 166.912 = 4005.888

Wait — actually better to do direct multiplication:

208.64 × 19.2
= 208.64 × (19 + 0.2)
= 208.64×19 = let’s compute:

200×19 = 3800
8.64×19 = 8×19=152; 0.64×19=12.16 → 152+12.16=164.16
So 3800 + 164.16 = 3964.16

Then 208.64 × 0.2 = 41.728

Total = 3964.16 + 41.728 = 4005.888

Now divide by 3:
4005.888 ÷ 3 = 1335.296 cm³

✔ Final Answer for #3: 1335.296

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Problem 4:
- Base: 17.7 in × 14.6 in
- Height: 18.9 in

Step 1: Base area = 17.7 × 14.6
Compute:

17 × 14.6 = 17×14 = 238; 17×0.6=10.2 → 248.2
0.7 × 14.6 = 10.22
Total = 248.2 + 10.22 = 258.42 in²

Step 2: Volume = (1/3) × 258.42 × 18.9
First, 258.42 × 18.9
Break into: 258.42 × 19 minus 258.42 × 0.1

258.42 × 19:
258.42 × 20 = 5168.4
Minus 258.42 = 5168.4 - 258.42 = 4909.98

Then subtract 258.42 × 0.1 = 25.842
So 4909.98 - 25.842 = 4884.138

Wait — no! That’s wrong logic.

Actually: 18.9 = 19 - 0.1? No, 19 - 0.1 = 18.9 yes, but we’re multiplying by 18.9, not subtracting.

Better: 258.42 × 18.9 = 258.42 × (18 + 0.9)

258.42 × 18:
258.42 × 10 = 2584.2
258.42 × 8 = 2067.36
Sum: 2584.2 + 2067.36 = 4651.56

258.42 × 0.9 = 232.578

Total = 4651.56 + 232.578 = 4884.138

Now divide by 3:
4884.138 ÷ 3 = 1628.046 in³

✔ Final Answer for #4: 1628.046

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Problem 5:
- Base: 20 mm × 16.3 mm
- Height: 24.8 mm

Step 1: Base area = 20 × 16.3 = 326 mm²

Step 2: Volume = (1/3) × 326 × 24.8
First, 326 × 24.8
Break: 326 × 25 = 8150
Minus 326 × 0.2 = 65.2
So 8150 - 65.2 = 8084.8

Wait — 24.8 = 25 - 0.2? Yes.

But 326 × 25 = 8150
326 × 0.2 = 65.2
So 326 × 24.8 = 8150 - 65.2 = 8084.8

Now divide by 3:
8084.8 ÷ 3 = 2694.933... ≈ 2694.933 mm³

Let me check with exact calculation:

326 × 24.8 = 326 × (24 + 0.8) = 326×24 = 7824; 326×0.8=260.8 → total 8084.8 ✔️

8084.8 ÷ 3 = 2694.933...

We can write as 2694.933 or round if needed, but since others had 3 decimals, keep it.

✔ Final Answer for #5: 2694.933

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Problem 6:
- Base: 13.6 m × 10.8 m
- Height: 13.5 m

Step 1: Base area = 13.6 × 10.8
Compute:

13 × 10.8 = 140.4
0.6 × 10.8 = 6.48
Total = 140.4 + 6.48 = 146.88 m²

Step 2: Volume = (1/3) × 146.88 × 13.5
First, 146.88 × 13.5
Break: 146.88 × 13 = ?

146.88 × 10 = 1468.8
146.88 × 3 = 440.64
Sum = 1468.8 + 440.64 = 1909.44

Then 146.88 × 0.5 = 73.44

Total = 1909.44 + 73.44 = 1982.88

Now divide by 3:
1982.88 ÷ 3 = 660.96 m³

✔ Final Answer for #6: 660.96

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Final Answers:

1) 428.064
2) 796.62
3) 1335.296
4) 1628.046
5) 2694.933
6) 660.96

All units are cubic units as given (ft³, m³, etc.)

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Final Answer:
1) 428.064
2) 796.62
3) 1335.296
4) 1628.046
5) 2694.933
6) 660.96