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 calculate carefully for each.
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1a. Surface Area (dimensions: 5, 3, 7)
Use surface area formula:
= 2×(5×3 + 5×7 + 3×7)
= 2×(15 + 35 + 21)
= 2×(71)
=
142
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1b. Volume (dimensions: 8, 7, 5)
Volume = 8 × 7 × 5
First, 8×7 = 56
Then, 56×5 =
280
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2a. Volume (dimensions: 7, 5, 8)
Volume = 7 × 5 × 8
7×5 = 35
35×8 =
280
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2b. Surface Area (dimensions: 8, 2, 7)
Surface area = 2×(8×2 + 8×7 + 2×7)
= 2×(16 + 56 + 14)
= 2×(86)
=
172
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3a. Surface Area (dimensions: 8, 4, 1)
Surface area = 2×(8×4 + 8×1 + 4×1)
= 2×(32 + 8 + 4)
= 2×(44)
=
88
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3b. Surface Area (dimensions: 1, 5, 4)
Surface area = 2×(1×5 + 1×4 + 5×4)
= 2×(5 + 4 + 20)
= 2×(29)
=
58
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Final Answer:
1a. 142
1b. 280
2a. 280
2b. 172
3a. 88
3b. 58
Parent Tip: Review the logic above to help your child master the concept of geometry surface area and volume worksheet answers.
