Introduction to Surface Area

Show your work for each problem.

1.
What does surface area measure?
1. a)The space inside a 3D shape
2. b)The length of a shape
3. c)The weight of a shape
4. d)The total area covering the outside of a 3D shape
Answer: The total area covering the outside of a 3D shape
Surface area measures the total area covering the outside of a 3D shape, like the amount of wrapping paper needed for a box.
2.
How many faces does a cube have?
1. a)8
2. b)5
3. c)4
4. d)6
Answer: 6
A cube has 6 faces: top, bottom, front, back, left, and right. That's why the surface area formula for a cube is .
3.
A cube has sides of 2 cm. What is the area of ONE face? (Just the number, in )
Answer: 4
Each face of a cube is a square. Area = .
4.
Find the surface area of a cube with side length 3 cm. (Just the number)
Answer: 54
Surface area = .
5.
What units do we use to measure surface area?
1. a)Meters (m)
2. b)Centimeters (cm)
3. c)Cubic centimeters ()
4. d)Square centimeters ()
Answer: Square centimeters ()
Surface area is measured in square units like or . Cubic units are for volume.
6.
Find the surface area of a cube with side length 5 cm.
Answer: 150
1. What is the formula for surface area of a cube? 6s^2
2. What is ? 25
3. What is ? 150
7.
A rectangular box has length 4 cm, width 2 cm, and height 3 cm. What is its surface area? (Just the number)
Answer: 52
SA = .
8.
A rectangular box has length 6 cm, width 4 cm, and height 2 cm. Find its surface area.
Answer: 88
1. Calculate the area of top and bottom faces: 48
2. Calculate the area of front and back faces: 24
3. Calculate the area of left and right faces: 16
4. Add all face areas: 88
9.
Which formula is used to find the surface area of a rectangular prism?
1. a)
2. b)
3. c)
4. d)
Answer:
The formula adds the areas of all 3 pairs of faces. is for volume, not surface area.
10.
A gift box is 10 cm long, 8 cm wide, and 5 cm tall. How much wrapping paper is needed to cover it?
Answer: 340
1. Area of top and bottom: 160
2. Area of front and back: 100
3. Area of left and right: 80
4. Total surface area: 340
11.
A cube has a surface area of . What is the length of each side? (Just the number)
Answer: 4
, so . Therefore cm.
12.
A room is 5 m long, 4 m wide, and 3 m high. You need to paint all 4 walls (not ceiling or floor). What is the total wall area?
Answer: 54
1. How many long walls are there (5m by 3m)? 2
2. Area of both long walls: 30
3. Area of both short walls: 24
4. Total wall area: 54
13.
If you double the side length of a cube, what happens to its surface area?
1. a)It quadruples (4 times)
2. b)It triples
3. c)It doubles
4. d)It stays the same
Answer: It quadruples (4 times)
If you double , the new SA = . It quadruples because area involves squaring the length.
14.
An open-top box (no lid) has length 12 cm, width 8 cm, and height 6 cm. What is its surface area?
Answer: 336
1. Calculate full surface area first: 432
2. What is the area of the missing top? 96
3. Subtract the top: 336
15.
A storage container has dimensions 3 m by 2 m by 2 m. If 1 liter of paint covers , how many liters are needed to paint the entire outside?
Answer: 6.4
SA = . Paint needed: liters.