7th grade · Math · Unit 6 of 17
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.
Alaska content standards learning standard: 7.G.6 · volume of prisms in problems with three-dimensional figures
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 Alaska
In the Alaska content standards, this is unit 6 of 17 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.
Source: Alaska Department of Education and Early Development
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 cylinder has a radius of 5 cm and a height of 14 cm. What is its volume? Use 3.14 for π and round to one decimal place.
answer boxcm³
1099.0 cm³
Hint: V = π × r × r × h ≈ 3.14 × 5 × 5 × 14 = 3.14 × 350 = 1099. Rounded: 1099.0 cm³.
Question 2
Which container holds more? (Use 3.14 for π.)
Container Shape Size Can Cylinder r = 4 cm, h = 5 cm Box Rectangular prism 5 cm × 4 cm × 11 cm - The can
- The box
- They hold the same amount
The can
Hint: Can: 3.14 × 4 × 4 × 5 = 251.2 cm³. Box: 5 × 4 × 11 = 220 cm³. The can holds more.
Question 3
A cylinder's circular base has an area of 113.04 cm². The cylinder is 12 cm tall. What is its volume?
- 4259.35 cm³
- 125.04 cm³
- 1356.48 cm³
- 678.24 cm³
1356.48 cm³
Hint: Volume = base area × height = 113.04 × 12 = 1356.48 cm³. The base area already includes π, so don't multiply by 3.14 again.
Question 4
A cube has edges 10 cm long. What is its volume?
- 120 cm³
- 600 cm³
- 100 cm³
- 1000 cm³
1000 cm³
Hint: All three dimensions are 10 cm: V = 10 × 10 × 10 = 1000 cm³. (100 is the area of one face.)
Question 5
What does the volume of a container tell you?
- How tall it is
- How much area its base covers
- 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 6
A box has a volume of 297 cm³. It is 11 cm long and 3 cm wide. How tall is it?
answer boxcm
9 cm
Hint: V = l × w × h, so 297 = 11 × 3 × h = 33 × h. Divide: h = 297 ÷ 33 = 9 cm.