Volume of Rectangular Prisms

Show your work for each problem.

1.
What is the formula for the volume of a rectangular prism?
1. a)
2. b)
3. c)
4. d)
Answer:
The volume of a rectangular prism is found by multiplying length × width × height: .
2.
A box has length 4 cm, width 3 cm, and height 2 cm. What is its volume in cm³?
Answer: 24
cm³. First multiply , then .
3.
What is the volume of a cube with side length 5 cm?
Answer: 125
cm³.
4.
Which unit is correct for measuring volume?
1. a)cm²
2. b)cm³
3. c)cm⁴
4. d)cm
Answer: cm³
Volume is measured in cubic units (cm³) because it represents three dimensions: length × width × height.
5.
A gift box measures 10 cm × 8 cm × 6 cm. Calculate its volume.
Answer: 480
1. What is 10 × 8? 80
2. What is 80 × 6? 480
6.
A storage container is 12 m long, 5 m wide, and 3 m high. What is its volume in m³?
Answer: 180
m³. The container has a volume of 180 cubic meters.
7.
A cube has a volume of 64 cm³. What is the length of one side?
1. a)2 cm
2. b)8 cm
3. c)16 cm
4. d)4 cm
Answer: 4 cm
Since and , we need . Since , the side is 4 cm.
8.
A rectangular box has volume 360 cm³. Its length is 12 cm and width is 6 cm. Find the height.
Answer: 5
1. What is 12 × 6 (the base area)? 72
2. What is 360 ÷ 72? 5
9.
An aquarium is 50 cm long, 25 cm wide, and 30 cm tall. How many liters can it hold? (1 liter = 1000 cm³)
Answer: 37.5
cm³. Converting to liters: liters.
10.
A swimming pool is 15 m long, 8 m wide, and 2 m deep. How many cubic meters of water does it hold?
Answer: 240
1. What is 15 × 8? 120
2. What is 120 × 2? 240
11.
A rectangular prism has dimensions 2.5 cm × 4 cm × 6 cm. What is its volume?
Answer: 60
cm³.
12.
Two cubes have sides of 3 cm and 4 cm. How much larger is the volume of the bigger cube?
Answer: 37
1. What is (volume of smaller cube)? 27
2. What is (volume of larger cube)? 64
3. What is 64 - 27? 37
13.
If you double all three dimensions of a rectangular prism, how many times larger is the new volume?
1. a)4 times
2. b)6 times
3. c)2 times
4. d)8 times
Answer: 8 times
New volume = original volume. Doubling each dimension multiplies volume by .
14.
A shipping box can hold 1800 cm³. If the length is 15 cm and width is 12 cm, what is the maximum height of items that can fit?
Answer: 10
1. What is 15 × 12 (the base area)? 180
2. What is 1800 ÷ 180? 10
15.
A concrete slab needs to be 6 m long, 4 m wide, and 0.25 m thick. How many cubic meters of concrete are needed?
Answer: 6
m³ of concrete needed.
16.
A box holds 24 small cubes, each with 2 cm sides. What is the total volume of all the cubes?
Answer: 192
1. What is the volume of one small cube ()? 8
2. What is 24 × 8? 192