Volume Basics
Question:
A solid is built from 24 unit cubes.
What is its volume?
24 cubic units
Question:
Find the volume of a rectangular prism with dimensions:
5 ft × 4 ft × 3 ft
Answer: 60 cubic feet
5 × 4 × 3 = 60 ft³
Question:
A cube has an edge length of 4 inches.
What is its volume?
Answer: 64 cubic inches
4 × 4 × 4 = 64 in³
Question:
A solid is made from two rectangular prisms.
The first prism has a volume of 48 cubic centimeters.
The second prism has a volume of 32 cubic centimeters.
What is the total volume?
Answer: 80 cubic centimeters
48 + 32 = 80 cm³
Question:
A student says:
“A box that is 5 cm × 4 cm × 3 cm has a volume of 12 cm³ because 5 + 4 + 3 = 12.”
Is the student correct?
Answer: No.
Volume is found by multiplying, not adding.
5 × 4 × 3 = 60 cm³
A rectangular prism is 6 units long, 4 units wide, and 3 units high.
What is its volume?
72 cubic units
A storage box measures 9 inches long, 6 inches wide, and 2 inches high.
What is its volume?
Answer: 108 cubic inches
9 × 6 × 2 = 108 in³
Question:
A cube has an edge length of 7 centimeters.
What is its volume?
Answer: 343 cubic centimeters
7 × 7 × 7 = 343 cm³
Answer: 80 cubic centimeters
48 + 32 = 80 cm³
Question:
A sculpture is made from two rectangular prisms.
What is the total volume?
Answer: 140 cubic units
Bottom:
10 × 4 × 2 = 80
Top:
5 × 4 × 3 = 60
Total:
80 + 60 = 140 cubic units
Question:
Two rectangular prisms have the same length and width.
One is 2 cm tall and the other is 5 cm tall.
Which one has the greater volume?
Answer: The prism that is 5 cm tall.
They have the same base area, but the second prism is taller, so it contains more cubic units.
A box has a length of 8 cm, a width of 5 cm, and a height of 4 cm.
What is its volume?
160 cubic cm
Question:
A fish tank has a length of 10 feet, a width of 4 feet, and a height of 3 feet.
How much space is inside the tank?
Answer: 120 cubic feet
10 × 4 × 3 = 120 ft³
Question:
A cube has a volume of 125 cubic inches.
What is the length of each edge?
Answer: 5 inches
Because:
5 × 5 × 5 = 125
Answer: 5 inches
Because:
5 × 5 × 5 = 125
Question:
A large block measures 12 cm × 8 cm × 6 cm.
A smaller block measuring 4 cm × 3 cm × 2 cm is removed.
What is the volume of the solid that remains?
Answer: 552 cubic centimeters
Large block:
12 × 8 × 6 = 576 cm³
Removed block:
4 × 3 × 2 = 24 cm³
Remaining:
576 − 24 = 552 cm³
Question:
A student says:
“If I double the length of a rectangular prism, its volume will always double.”
Is the student correct?
Answer: Yes, as long as the width and height stay the same.
For example:
Original:
4 × 3 × 2 = 24 cm³
Double the length:
8 × 3 × 2 = 48 cm³
The volume doubled from 24 to 48 cm³.
A rectangular prism has a volume of 180 cubic meters.
Its length is 9 meters and its width is 5 meters.
What is its height?
4 meters
Question:
A rectangular prism has a volume of 336 cubic centimeters.
Its dimensions are 8 cm × 7 cm × ?
What is the missing dimension?
Answer: 6 centimeters
8 × 7 = 56
336 ÷ 56 = 6 cm
A cube has a volume of 216 cubic centimeters.
What is the length of each edge?
Answer: 6 centimeters
Because:
6 × 6 × 6 = 216
A wooden block measures 15 cm × 10 cm × 8 cm.
A rectangular section measuring 5 cm × 4 cm × 3 cm is cut out.
What is the volume of the remaining wood?
Answer: 1,140 cubic centimeters
Original:
15 × 10 × 8 = 1,200 cm³
Cut out:
5 × 4 × 3 = 60 cm³
Remaining:
1,200 − 60 = 1,140 cm³
Question:
A student calculates the volume of a box:
10 × 6 × 4 = 240
Then writes:
240 square centimeters
What is the mistake?
Answer: The unit should be cubic centimeters, not square centimeters.
Volume measures three-dimensional space, so the correct answer is:
240 cubic centimeters (cm³)
Question:
A rectangular prism has dimensions of 12 cm × 7 cm × 5 cm.
Another prism has dimensions of 10 cm × 6 cm × 6 cm.
Which prism has the greater volume, and by how much?
Answer: The first prism by 60 cm³
First prism:
12 × 7 × 5 = 420 cm³
Second prism:
10 × 6 × 6 = 360 cm³
Difference:
420 − 360 = 60 cm³
A rectangular swimming pool is 15 meters long and 8 meters wide.
It has a volume of 720 cubic meters.
How deep is the pool?
Answer: 6 centimeters
8 × 7 = 56
336 ÷ 56 = 6 cm
Answer: 6 meters
First find the area of the base:
15 × 8 = 120 m²
Then:
720 ÷ 120 = 6 m
Question:
You build a cube using 512 unit cubes.
How many unit cubes are along each edge of the cube?
Answer: 8 unit cubes
You need a number that multiplied by itself three times equals 512:
8 × 8 × 8 = 512
So there are 8 cubes along each edge.
Question:
A sculpture is made from two rectangular prisms.
Prism A:
12 cm long × 6 cm wide × 4 cm high
Prism B:
6 cm long × 3 cm wide × 5 cm high
What is the total volume of the sculpture?
Answer: 378 cubic centimeters
Prism A:
12 × 6 × 4 = 288 cm³
Prism B:
6 × 3 × 5 = 90 cm³
Total:
288 + 90 = 378 cm³
Question:
A rectangular tank has three pairs of faces.
The areas of the three different faces are:
What is the volume of the tank?
Answer: 72 cubic centimeters
The three face areas represent:
length × width = 12
length × height = 18
width × height = 24
To find the volume, multiply the three face areas and take the square root:
12 × 18 × 24 = 5,184
√5,184 = 72
Final Answer: 72 cm³