Let’s solve each problem step by step. We’ll find the
volume and
surface area for each rectangular prism.
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🔢 Formulas to remember:
-
Volume = length × width × height
(V = l × w × h)
-
Surface Area = 2×(lw + lh + wh)
(Add up the areas of all 6 faces — front/back, left/right, top/bottom)
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## Problem 1:
Dimensions: 3 in × 3 in × 5 in
✔ Volume = 3 × 3 × 5 = 9 × 5 =
45 cubic inches
✔ Surface Area = 2×(3×3 + 3×5 + 3×5)
= 2×(9 + 15 + 15)
= 2×(39) =
78 square inches
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## Problem 2:
Dimensions: 4 in × 2 in × 4 in
✔ Volume = 4 × 2 × 4 = 8 × 4 =
32 cubic inches
✔ Surface Area = 2×(4×2 + 4×4 + 2×4)
= 2×(8 + 16 + 8)
= 2×(32) =
64 square inches
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## Problem 3:
Dimensions: 5 in × 4 in × 6 in
✔ Volume = 5 × 4 × 6 = 20 × 6 =
120 cubic inches
✔ Surface Area = 2×(5×4 + 5×6 + 4×6)
= 2×(20 + 30 + 24)
= 2×(74) =
148 square inches
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## Problem 4:
Dimensions: 5 in × 7 in × 8 in
✔ Volume = 5 × 7 × 8 = 35 × 8 =
280 cubic inches
✔ Surface Area = 2×(5×7 + 5×8 + 7×8)
= 2×(35 + 40 + 56)
= 2×(131) =
262 square inches
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Final Answer:
1. Volume: 45 in³, Surface Area: 78 in²
2. Volume: 32 in³, Surface Area: 64 in²
3. Volume: 120 in³, Surface Area: 148 in²
4. Volume: 280 in³, Surface Area: 262 in²
Parent Tip: Review the logic above to help your child master the concept of surface area worksheet 5th grade.
