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.
Maine Learning Results learning standard: 7.G.B.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 Maine
In the Maine Learning Results, 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: Maine Department of Education
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 cube has edges 9 cm long. What is its volume?
- 108 cm³
- 81 cm³
- 729 cm³
- 486 cm³
729 cm³
Hint: All three dimensions are 9 cm: V = 9 × 9 × 9 = 729 cm³. (81 is the area of one face.)
Question 2
A cylinder has a radius of 6 cm and a height of 12 cm. What is its volume? Use 3.14 for π and round to one decimal place.
answer boxcm³
1356.5 cm³
Hint: V = π × r × r × h ≈ 3.14 × 6 × 6 × 12 = 3.14 × 432 = 1356.48. Rounded: 1356.5 cm³.
Question 3
Which formula gives the volume of a cylinder?
- V = π × d × h
- V = l × w × h
- V = π × r × r × h
- V = 2 × π × r × h
V = π × r × r × h
Hint: Volume = area of the base × height. A cylinder's base is a circle with area π × r × r.
Question 4
A box is 6 cm long, 11 cm wide and 8 cm high. What is its volume?
answer boxcm³
528 cm³
Hint: V = l × w × h = 6 × 11 × 8 = 66 × 8 = 528 cm³.
Question 5
A box has a volume of 243 cm³. It is 9 cm long and 9 cm wide. How tall is it?
answer boxcm
3 cm
Hint: V = l × w × h, so 243 = 9 × 9 × h = 81 × h. Divide: h = 243 ÷ 81 = 3 cm.
Question 6
Which container holds more? (Use 3.14 for π.)
Container Shape Size Can Cylinder r = 3 cm, h = 9 cm Box Rectangular prism 3 cm × 5 cm × 15 cm - They hold the same amount
- The can
- The box
The can
Hint: Can: 3.14 × 3 × 3 × 9 = 254.34 cm³. Box: 3 × 5 × 15 = 225 cm³. The can holds more.