I will solve the problem presented in the image, which is to find the volume and surface area for each of the four rectangular prisms shown. I'll work through each one step by step.
First, let's recall the formulas:
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Volume (V) of a rectangular prism: `V = length × width × height`
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Surface Area (SA) of a rectangular prism: `SA = 2lw + 2lh + 2wh`, where `l` is length, `w` is width, and `h` is height.
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Problem 1:
The dimensions are 8 in (length), 7 in (width), and 5 in (height).
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Volume: `V = 8 × 7 × 5 = 280 cubic inches`
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Surface Area: `SA = 2(8×7) + 2(8×5) + 2(7×5) = 2(56) + 2(40) + 2(35) = 112 + 80 + 70 = 262 square inches`
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Problem 2:
The dimensions are 5 in (length), 4 in (width), and 4 in (height).
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Volume: `V = 5 × 4 × 4 = 80 cubic inches`
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Surface Area: `SA = 2(5×4) + 2(5×4) + 2(4×4) = 2(20) + 2(20) + 2(16) = 40 + 40 + 32 = 112 square inches`
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Problem 3:
The dimensions are 4 in (length), 3 in (width), and 9 in (height).
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Volume: `V = 4 × 3 × 9 = 108 cubic inches`
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Surface Area: `SA = 2(4×3) + 2(4×9) + 2(3×9) = 2(12) + 2(36) + 2(27) = 24 + 72 + 54 = 150 square inches`
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Problem 4:
The dimensions are 8 in (length), 6 in (width), and 5 in (height).
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Volume: `V = 8 × 6 × 5 = 240 cubic inches`
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Surface Area: `SA = 2(8×6) + 2(8×5) + 2(6×5) = 2(48) + 2(40) + 2(30) = 96 + 80 + 60 = 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: 108 in³,
Surface Area: 150 in²
4.
Volume: 240 in³,
Surface Area: 236 in²
Parent Tip: Review the logic above to help your child master the concept of surface area worksheet with answers.
