Explanation:
We are given 5 right prisms (rectangular prisms — boxes) and asked to find the
surface area (SA) and
volume (V) for each.
Recall the formulas:
-
Volume of a rectangular prism = length × width × height
(Units: cubic units, e.g., cm³, in³)
-
Surface Area of a rectangular prism = 2(lw + lh + wh)
(Units: square units, e.g., cm², in²)
Let’s go one by one.
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1. Dimensions: 3 cm × 2 cm × 3 cm
Let l = 3 cm, w = 2 cm, h = 3 cm
Volume:
V = 3 × 2 × 3 = 18 cm³
Surface Area:
SA = 2[(3×2) + (3×3) + (2×3)] = 2[6 + 9 + 6] = 2 × 21 = 42 cm²
✔ SA = 42 cm², V = 18 cm³
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2. Dimensions: 5 in × 7 in × 4 in
l = 5, w = 7, h = 4
Volume:
V = 5 × 7 × 4 = 140 in³
Surface Area:
SA = 2[(5×7) + (5×4) + (7×4)] = 2[35 + 20 + 28] = 2 × 83 = 166 in²
✔ SA = 166 in², V = 140 in³
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3. Dimensions: 10 ft × 10 ft × 36 ft
l = 10, w = 10, h = 36
Volume:
V = 10 × 10 × 36 = 3600 ft³
Surface Area:
SA = 2[(10×10) + (10×36) + (10×36)] = 2[100 + 360 + 360] = 2 × 820 = 1640 ft²
✔ SA = 1640 ft², V = 3600 ft³
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4. Dimensions: 27 cm × 4.5 cm × 3.5 cm
Let’s compute carefully.
Volume:
V = 27 × 4.5 × 3.5
First, 27 × 4.5 = 27 × (9/2) = (27×9)/2 = 243/2 = 121.5
Then, 121.5 × 3.5 = 121.5 × (7/2) = (121.5 × 7)/2 = 850.5 / 2 = 425.25 cm³
Or do decimal:
27 × 4.5 = 121.5
121.5 × 3.5 = 121.5 × 3 + 121.5 × 0.5 = 364.5 + 60.75 = 425.25 cm³
✔
Surface Area:
SA = 2[(27×4.5) + (27×3.5) + (4.5×3.5)]
Compute each:
- 27 × 4.5 = 121.5
- 27 × 3.5 = 94.5
- 4.5 × 3.5 = 15.75
Sum = 121.5 + 94.5 + 15.75 = 231.75
SA = 2 × 231.75 = 463.5 cm²
✔
✔ SA = 463.5 cm², V = 425.25 cm³
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5. Dimensions: 28 in × 1.25 in × 1.25 in
Note: two sides are equal (square cross-section).
Volume:
V = 28 × 1.25 × 1.25
1.25 × 1.25 = 1.5625
28 × 1.5625 = let’s compute:
28 × 1 = 28
28 × 0.5 = 14
28 × 0.0625 = 28 × (1/16) = 28/16 = 1.75
So total = 28 + 14 + 1.75 = 43.75 in³
Alternatively: 1.5625 × 28 = (15625/10000) × 28 = (15625 × 28)/10000 = 437500 / 10000 = 43.75
✔
Surface Area:
SA = 2[(28×1.25) + (28×1.25) + (1.25×1.25)]
= 2[35 + 35 + 1.5625]
= 2[71.5625] = 143.125 in²
Check:
28 × 1.25 = 35 (yes)
1.25 × 1.25 = 1.5625
Sum inside = 35 + 35 + 1.5625 = 71.5625
×2 = 143.125
✔
✔ SA = 143.125 in², V = 43.75 in³
Now compile all answers clearly:
1. SA = 42 cm², V = 18 cm³
2. SA = 166 in², V = 140 in³
3. SA = 1640 ft², V = 3600 ft³
4. SA = 463.5 cm², V = 425.25 cm³
5. SA = 143.125 in², V = 43.75 in³
Final Answer:
1. SA = 42 cm², V = 18 cm³
2. SA = 166 in², V = 140 in³
3. SA = 1640 ft², V = 3600 ft³
4. SA = 463.5 cm², V = 425.25 cm³
5. SA = 143.125 in², V = 43.75 in³
Parent Tip: Review the logic above to help your child master the concept of geometry surface area worksheet.
