Here are the step-by-step solutions for each problem on the worksheet.
1 a. Find the surface area
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Dimensions: Length = 7, Width = 3, Height = 5
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Formula: Surface Area = $2(lw + lh + wh)$
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Step 1: Calculate the area of the three pairs of faces.
* $7 \times 3 = 21$
* $7 \times 5 = 35$
* $3 \times 5 = 15$
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Step 2: Add them together.
* $21 + 35 + 15 = 71$
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Step 3: Multiply by 2.
* $71 \times 2 = 142$
1 b. Find the volume
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Dimensions: Length = 7, Width = 5, Height = 8
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Formula: Volume = $l \times w \times h$
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Calculation:
* $7 \times 5 = 35$
* $35 \times 8 = 280$
2 a. Find the volume
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Dimensions: Length = 8, Width = 5, Height = 7
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Formula: Volume = $l \times w \times h$
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Calculation:
* $8 \times 5 = 40$
* $40 \times 7 = 280$
2 b. Find the surface area
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Dimensions: Length = 7, Width = 2, Height = 8
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Formula: Surface Area = $2(lw + lh + wh)$
*
Step 1: Calculate the area of the face pairs.
* $7 \times 2 = 14$
* $7 \times 8 = 56$
* $2 \times 8 = 16$
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Step 2: Add them together.
* $14 + 56 + 16 = 86$
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Step 3: Multiply by 2.
* $86 \times 2 = 172$
3 a. Find the surface area
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Dimensions: Length = 4, Width = 1, Height = 8
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Formula: Surface Area = $2(lw + lh + wh)$
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Step 1: Calculate the area of the face pairs.
* $4 \times 1 = 4$
* $4 \times 8 = 32$
* $1 \times 8 = 8$
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Step 2: Add them together.
* $4 + 32 + 8 = 44$
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Step 3: Multiply by 2.
* $44 \times 2 = 88$
3 b. Find the surface area
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Dimensions: Length = 5, Width = 4, Height = 1
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Formula: Surface Area = $2(lw + lh + wh)$
*
Step 1: Calculate the area of the face pairs.
* $5 \times 4 = 20$
* $5 \times 1 = 5$
* $4 \times 1 = 4$
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Step 2: Add them together.
* $20 + 5 + 4 = 29$
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Step 3: Multiply by 2.
* $29 \times 2 = 58$
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Final Answer:
1 a. 142
1 b. 280
2 a. 280
2 b. 172
3 a. 88
3 b. 58
Parent Tip: Review the logic above to help your child master the concept of surface area and volume worksheets.
