Surface Area of Cubes

Show your work for each problem.

1.
How many faces does a cube have?
1. a)12
2. b)6
3. c)4
4. d)8
Answer: 6
A cube has 6 identical square faces: top, bottom, front, back, left, and right.
2.
What is the formula for the surface area of a cube with side length ?
1. a)
2. b)
3. c)
4. d)
Answer:
Surface area = 6 faces area of one face = . Note: is the formula for volume, not surface area!
3.
A cube has sides of 2 cm. What is its surface area in cm²?
Answer: 24
SA = cm²
4.
Calculate the surface area of a cube with side length 3 meters. Give your answer in m².
Answer: 54
SA = m²
5.
Find the surface area of a cube with side length 5 cm.
Answer: 150
1. What is the side length of the cube? 5
2. What is ? 25
3. Multiply by 6. What is ? 150
6.
A cube has a surface area of 96 cm². What is the side length in cm?
Answer: 4
cm
7.
Which cube has a greater surface area: one with side 4 cm or one with side 5 cm?
1. a)They are equal
2. b)Side 5 cm (SA = 150 cm²)
3. c)Side 4 cm (SA = 96 cm²)
4. d)Cannot be determined
Answer: Side 5 cm (SA = 150 cm²)
Side 4 cm: cm². Side 5 cm: cm². The 5 cm cube has more surface area.
8.
A cube has a surface area of 294 cm². Find the side length.
Answer: 7
1. Write the equation: . Divide both sides by 6. What is ? 49
2. Now we have . What is ? 7
9.
A cube has edges of 10 cm. What is the surface area in cm²?
Answer: 600
SA = cm²
10.
Calculate the surface area of a cube with side length 8 cm.
Answer: 384
1. What is ? 64
2. Multiply by 6. What is ? 384
11.
If you double the side length of a cube, what happens to its surface area?
1. a)It quadruples (becomes 4 times larger)
2. b)It doubles
3. c)It becomes 8 times larger
4. d)It triples
Answer: It quadruples (becomes 4 times larger)
If side doubles from to : New SA = . The surface area becomes 4 times larger!
12.
You need to wrap a cubic gift box with 6 cm edges. How many square centimeters of wrapping paper do you need?
Answer: 216
1. What is the side length of the cube? 6
2. What is ? 36
3. Multiply by 6 for all faces. What is ? 216
13.
A cube has a surface area of 486 m². What is the side length in meters?
Answer: 9
m
14.
A cubic container with 4 m edges needs to be painted. One can of paint covers 20 m². How many cans are needed?
Answer: 5
1. Calculate the surface area. What is ? 96
2. Divide by coverage per can. What is ? 4.8
3. Round up (you can't buy partial cans). How many cans do you need? 5
15.
What units should surface area be measured in?
1. a)cm, m, in (linear units)
2. b)Any units work
3. c)cm³, m³, in³ (cubic units)
4. d)cm², m², in² (square units)
Answer: cm², m², in² (square units)
Surface area is 2-dimensional (length width), so it uses square units like cm², m², or in². Linear units (cm) are for length, and cubic units (cm³) are for volume.
16.
Compare the surface areas of two cubes: one with side 3 cm and one with side 6 cm. How many times larger is the bigger cube's surface area?
Answer: 4
1. Calculate SA of 3 cm cube: 54
2. Calculate SA of 6 cm cube: 216
3. Divide to compare: 4
17.
A cube has a surface area of 600 cm². What is the side length in cm?
Answer: 10
cm