Let's solve each problem step by step using the formulas for
surface area and
volume of a rectangular prism.
---
🔷 Formulas:
-
Volume (V) of a rectangular prism = $ V = l \times w \times h $
-
Surface Area (SA) of a rectangular prism = $ SA = 2(lw + lh + wh) $
Where:
- $ l $ = length
- $ w $ = width
- $ h $ = height
---
##
✔ Problem 1a: Surface Area of Rectangular Prism
Dimensions:
Length = 7, Width = 3, Height = 4
(From the diagram: 7 on the front, 3 on the base, 4 on the side)
$$
SA = 2(lw + lh + wh)
= 2(7 \times 3 + 7 \times 4 + 3 \times 4)
= 2(21 + 28 + 12)
= 2(61)
= \boxed{122}
$$
✔ Answer: 122 square units
---
##
✔ Problem 1b: Volume of Rectangular Prism
Dimensions:
Length = 7, Width = 5, Height = 6
(From diagram: 7 on front, 5 on side, 6 on vertical edge)
$$
V = l \times w \times h = 7 \times 5 \times 6 = 210
$$
✔ Answer: 210 cubic units
---
##
✔ Problem 2a: Volume of Rectangular Prism
Dimensions:
Length = 8, Width = 5, Height = 7
$$
V = 8 \times 5 \times 7 = 280
$$
✔ Answer: 280 cubic units
---
##
✔ Problem 2b: Surface Area of Rectangular Prism
Dimensions:
Length = 7, Width = 2, Height = 9
$$
SA = 2(lw + lh + wh)
= 2(7 \times 2 + 7 \times 9 + 2 \times 9)
= 2(14 + 63 + 18)
= 2(95)
= \boxed{190}
$$
✔ Answer: 190 square units
---
##
✔ Problem 3a: Surface Area of Rectangular Prism
Dimensions:
Length = 4, Width = 1, Height = 6
$$
SA = 2(lw + lh + wh)
= 2(4 \times 1 + 4 \times 6 + 1 \times 6)
= 2(4 + 24 + 6)
= 2(34)
= \boxed{68}
$$
✔ Answer: 68 square units
---
##
✔ Problem 3b: Surface Area of Rectangular Prism
Dimensions:
Length = 5, Width = 4, Height = 1
(Note: The top face shows 4 and 5, and height is 1)
$$
SA = 2(lw + lh + wh)
= 2(5 \times 4 + 5 \times 1 + 4 \times 1)
= 2(20 + 5 + 4)
= 2(29)
= \boxed{58}
$$
✔ Answer: 58 square units
---
📝 Final Answers:
| Problem | Answer |
|--------|--------|
| 1a | 122 sq units |
| 1b | 210 cu units |
| 2a | 280 cu units |
| 2b | 190 sq units |
| 3a | 68 sq units |
| 3b | 58 sq units |
Let me know if you'd like these written out in a printable format or explained further!
Parent Tip: Review the logic above to help your child master the concept of volume and surface area worksheets.
