Volume and surface area worksheet for calculating dimensions of rectangular prisms.

Let’s solve each problem one by one. We’ll use the formulas:

- Volume of a rectangular prism = length × width × height
- Surface area of a rectangular prism = 2×(length×width + length×height + width×height)

We’ll go step by step for each part.

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1a. Find the surface area of this rectangular prism.
Dimensions: 5, 3, 7 (let’s say length=7, width=3, height=5 — order doesn’t matter as long as we’re consistent)

Surface Area = 2×(lw + lh + wh)
= 2×(7×3 + 7×5 + 3×5)
= 2×(21 + 35 + 15)
= 2×(71)
= 142

✔ Double-check: 21+35=56; 56+15=71; 71×2=142 → Correct.

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1b. Find the volume of this rectangular prism.
Dimensions: 8, 7, 5

Volume = l × w × h = 8 × 7 × 5
First: 8×7 = 56
Then: 56×5 = 280

✔ Double-check: 56×5 = 280 → Correct.

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2a. Find the volume of this rectangular prism.
Dimensions: 7, 5, 8

Volume = 7 × 5 × 8
7×5 = 35
35×8 = 280

✔ Double-check: 35×8 = 280 → Correct.

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2b. Find the surface area of this rectangular prism.
Dimensions: 8, 2, 7

Surface Area = 2×(lw + lh + wh)
Let’s assign: l=8, w=2, h=7
= 2×(8×2 + 8×7 + 2×7)
= 2×(16 + 56 + 14)
= 2×(86)
= 172

✔ Double-check: 16+56=72; 72+14=86; 86×2=172 → Correct.

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3a. Find the surface area of this rectangular prism.
Dimensions: 8, 4, 1

Surface Area = 2×(lw + lh + wh)
l=8, w=4, h=1
= 2×(8×4 + 8×1 + 4×1)
= 2×(32 + 8 + 4)
= 2×(44)
= 88

✔ Double-check: 32+8=40; 40+4=44; 44×2=88 → Correct.

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3b. Find the surface area of this rectangular prism.
Dimensions: 5, 4, 1

Surface Area = 2×(lw + lh + wh)
l=5, w=4, h=1
= 2×(5×4 + 5×1 + 4×1)
= 2×(20 + 5 + 4)
= 2×(29)
= 58

✔ Double-check: 20+5=25; 25+4=29; 29×2=58 → Correct.

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Final Answer:
1a. 142
1b. 280
2a. 280
2b. 172
3a. 88
3b. 58