Surface Area of Rectangular Prisms

Show your work for each problem.

1.
A rectangular prism has 6 faces. How do they come in groups?
1. a)6 different faces
2. b)2 groups of 3 faces
3. c)1 pair and 4 single faces
4. d)3 pairs of matching faces
Answer: 3 pairs of matching faces
A rectangular prism has 3 pairs of matching faces: top/bottom (), front/back (), and left/right (). This is why we multiply by 2 in the formula.
2.
What units are used to measure surface area?
1. a)Cubic units (cm³, m³)
2. b)Linear units (cm, m)
3. c)Square units (cm², m²)
4. d)No units needed
Answer: Square units (cm², m²)
Surface area measures flat surfaces (2D), so we use square units like cm² or m². Volume uses cubic units, and length uses linear units.
3.
A cube has all sides equal to 2 cm. What is the area of ONE face?
Answer: 4
Each face of a cube is a square. Area = cm².
4.
A cube has sides of 3 cm. What is its total surface area? (Use SA = 6s²)
Answer: 54
SA = cm². All 6 faces are identical 3×3 squares.
5.
Find the surface area of a box with length 4 cm, width 3 cm, and height 2 cm.
Answer: 52
1. What is (top/bottom faces)? 12
2. What is (front/back faces)? 8
3. What is (left/right faces)? 6
4. What is ? 26
5. What is (final answer)? 52
6.
Which expression correctly represents the surface area of a box with length 5, width 4, and height 3?
1. a)
2. b)
3. c)
4. d)
Answer:
SA = . Option B is volume, C is just adding dimensions, D forgets to multiply by 2 for paired faces.
7.
A rectangular prism has dimensions 6 cm × 5 cm × 4 cm. Find its surface area.
Answer: 148
SA = cm²
8.
A gift box is 10 cm long, 8 cm wide, and 6 cm high. How many square centimeters of wrapping paper are needed?
Answer: 376
SA = cm²
9.
A storage container is 2 m long, 1.5 m wide, and 1 m high. Find its surface area in square meters.
Answer: 13
1. What is (top/bottom)? 3
2. What is (front/back)? 2
3. What is (sides)? 1.5
4. What is ? 6.5
5. What is ? 13
10.
One can of paint covers 50 m². The surface area of a room's walls is 120 m². How many cans are needed?
1. a)3 cans
2. b)2 cans
3. c)4 cans
4. d)2.4 cans
Answer: 3 cans
cans. Since you can't buy 0.4 of a can, you need 3 full cans.
11.
An aquarium is 60 cm long, 30 cm wide, and 40 cm high. Find the surface area of all 6 sides.
Answer: 10800
1. Calculate (top/bottom faces) 1800
2. Calculate (front/back faces) 2400
3. Calculate (side faces) 1200
4. Add: 5400
5. Multiply by 2: 10800
12.
A rectangular prism has a surface area of 94 cm². Its length is 5 cm and width is 3 cm. What is its height?
Answer: 4
→ → → → cm
13.
If you double all dimensions of a rectangular prism, the surface area becomes:
1. a)6 times as large
2. b)2 times as large
3. c)8 times as large
4. d)4 times as large
Answer: 4 times as large
Each face area involves multiplying two dimensions. If both double, the area becomes times larger. This applies to all 6 faces, so total SA is 4 times larger.
14.
A box has length 8 cm, width 6 cm, and surface area 236 cm². Find the height.
Answer: 5
1. What is ? 48
2. Set up: . What is ? 14
3. Divide 236 by 2. What is 118? 118
4. Solve: . What is ? 70
5. What is ? 5
15.
A rectangular prism has dimensions 12 cm × 9 cm × 7 cm. What is its surface area?
Answer: 510
SA = cm²
16.
Two boxes have the same volume of 60 cm³. Box A is 5×4×3 cm. Box B is 6×5×2 cm. Which has greater surface area?
Answer: B
1. Calculate SA of Box A: . What is it? 94
2. Calculate SA of Box B: . What is it? 104
3. Which letter has the greater surface area: A or B? B