Volume vs Surface Area

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Show your work for each problem.

1.
You want to know how much water a fish tank can hold. Which measurement do you need?
1. a)Volume
2. b)Perimeter
3. c)Length
4. d)Surface area
2.
You want to wrap a gift box. Which measurement tells you how much wrapping paper you need?
1. a)Diagonal
2. b)Volume
3. c)Weight
4. d)Surface area
3.
A cube has a side length of 5 cm. What is its volume in cm³?
4.
A cube has a side length of 5 cm. What is its surface area in cm²?
5.
What unit is used for volume?
1. a)cm (linear)
2. b)kg (mass)
3. c)cm² (square)
4. d)cm³ (cubic)
6.
A rectangular box is 8 cm long, 5 cm wide, and 3 cm tall. Calculate both its volume and surface area.
7.
A painter needs to paint the walls of a room. Which measurement helps determine how much paint to buy?
1. a)Height of ceiling
2. b)Volume of room
3. c)Surface area of walls
4. d)Number of windows
8.
A box has dimensions 10 cm × 6 cm × 4 cm. What is its volume in cm³?
9.
A box has dimensions 10 cm × 6 cm × 4 cm. What is its surface area in cm²?
10.
Box A is 3×3×8 cm. Box B is 4×4×4.5 cm. Which has more volume? Which has more surface area?
11.
An air conditioning company sizes units based on room measurements. Should they use volume or surface area?
1. a)Volume - to cool the air inside
2. b)Perimeter - to measure the edges
3. c)Surface area - to cover the walls
4. d)Height only - that's what matters
12.
A swimming pool is 25m long, 10m wide, and 2m deep. How many liters of water does it hold? (1 m³ = 1000 liters)
13.
A warehouse floor is 50m × 30m. The walls are 8m high. What is the surface area of all 4 walls (not floor or ceiling) in m²?
14.
A cereal box is 20 cm × 6 cm × 30 cm. The company wants to reduce cardboard cost by 10%. What would the new surface area be in cm²?
15.
Which shape has the smallest surface area for a given volume?
1. a)Flat wide box
2. b)Long thin box
3. c)Cube
4. d)Sphere
16.
A juice box holds 250 mL. You want to know how much plastic covers the outside. Do you need volume or surface area?
17.
A gift box is 15 cm × 15 cm × 15 cm. How much wrapping paper (in cm²) is needed to cover all sides?
18.
A storage container is 2m × 1.5m × 1m. You need to: (a) Find how many cubic meters it can hold. (b) Find how much material covers all 6 sides.