I will solve the problem by calculating the volume and surface area for each of the four rectangular prisms shown in the worksheet. I'll use the standard formulas for a rectangular prism.
The formulas are:
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Volume (V) = Length × Width × Height
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Surface Area (SA) = 2 × (Length × Width + Length × Height + Width × Height)
I will calculate these for each prism one by one.
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Prism 1:
Dimensions: 8 in (length), 7 in (width), 5 in (height)
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Volume = 8 × 7 × 5 = 280 cubic inches
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Surface Area = 2 × (8×7 + 8×5 + 7×5) = 2 × (56 + 40 + 35) = 2 × 131 = 262 square inches
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Prism 2:
Dimensions: 5 in (length), 4 in (width), 4 in (height)
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Volume = 5 × 4 × 4 = 80 cubic inches
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Surface Area = 2 × (5×4 + 5×4 + 4×4) = 2 × (20 + 20 + 16) = 2 × 56 = 112 square inches
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Prism 3:
Dimensions: 4 in (length), 3 in (width), 3 in (height)
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Volume = 4 × 3 × 3 = 36 cubic inches
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Surface Area = 2 × (4×3 + 4×3 + 3×3) = 2 × (12 + 12 + 9) = 2 × 33 = 66 square inches
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Prism 4:
Dimensions: 8 in (length), 6 in (width), 5 in (height)
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Volume = 8 × 6 × 5 = 240 cubic inches
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Surface Area = 2 × (8×6 + 8×5 + 6×5) = 2 × (48 + 40 + 30) = 2 × 118 = 236 square inches
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Final Answers:
1.
Volume: 280 in³,
Surface Area: 262 in²
2.
Volume: 80 in³,
Surface Area: 112 in²
3.
Volume: 36 in³,
Surface Area: 66 in²
4.
Volume: 240 in³,
Surface Area: 236 in²
Parent Tip: Review the logic above to help your child master the concept of geometry volume and surface area math worksheet.
