7th grade · Math · Unit 6 of 18
Volume
Boxes, cubes and cylinders
What your child practices
Finding volume as base area × height for boxes and cylinders, working backwards to a missing dimension, and linking cm³ to milliliters and liters.
Alabama Course of Study content standard: 7.22 · volume of prisms in real-world problems
How we explain it
Children can open this short lesson before they practice.
- Volume is the amount of space inside a 3D object.
- For a prism: volume = area of the base × height.
- Volume is measured in cubic units, like cm³.
Example: A box is 4 cm long, 3 cm wide and 2 cm high. What is its volume? Base area: 4 × 3 = 12 cm². Volume: 12 × 2 = 24. Answer: 24 cm³
Volume in Alabama
In the Alabama Course of Study, this is unit 6 of 18 in 7th grade Math, after Circles and before Probability.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
A box is 11 cm long, 3 cm wide and 9 cm high. What is its volume?
answer boxcm³
297 cm³
Hint: V = l × w × h = 11 × 3 × 9 = 33 × 9 = 297 cm³.
Question 2
1000 cm³ holds 1 L. How many liters of water fill a fish tank 40 cm × 35 cm × 40 cm?
answer boxL
56 L
Hint: Volume: 40 × 35 × 40 = 56000 cm³. Divide by 1000 to change to liters: 56 L.
Question 3
What does the volume of a container tell you?
- How much area its base covers
- How tall it is
- How much space is inside it
- How far it is around the outside
How much space is inside it
Hint: Volume measures the space a 3-D object takes up or holds, in cubic units.
Question 4
A cylinder's circular base has an area of 28.26 cm². The cylinder is 5 cm tall. What is its volume?
- 443.68 cm³
- 70.65 cm³
- 33.26 cm³
- 141.3 cm³
141.3 cm³
Hint: Volume = base area × height = 28.26 × 5 = 141.3 cm³. The base area already includes π, so don't multiply by 3.14 again.
Question 5
Which container holds more? (Use 3.14 for π.)
Container Shape Size Can Cylinder r = 2 cm, h = 15 cm Box Rectangular prism 5 cm × 4 cm × 12 cm - They hold the same amount
- The box
- The can
The box
Hint: Can: 3.14 × 2 × 2 × 15 = 188.4 cm³. Box: 5 × 4 × 12 = 240 cm³. The box holds more.
Question 6
A box has a volume of 180 cm³. It is 2 cm long and 10 cm wide. How tall is it?
answer boxcm
9 cm
Hint: V = l × w × h, so 180 = 2 × 10 × h = 20 × h. Divide: h = 180 ÷ 20 = 9 cm.