7th grade · Math · Unit 6 of 16
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.
Arizona Academic Standards 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 Arizona
In the Arizona Academic Standards, this is unit 6 of 16 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: Arizona 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 cylinder's circular base has an area of 113.04 cm². The cylinder is 6 cm tall. What is its volume?
- 678.24 cm³
- 119.04 cm³
- 2129.67 cm³
- 339.12 cm³
678.24 cm³
Hint: Volume = base area × height = 113.04 × 6 = 678.24 cm³. The base area already includes π, so don't multiply by 3.14 again.
Question 2
1000 cm³ holds 1 L. How many liters of water fill a fish tank 25 cm × 30 cm × 40 cm?
answer boxL
30 L
Hint: Volume: 25 × 30 × 40 = 30000 cm³. Divide by 1000 to change to liters: 30 L.
Question 3
Which container holds more? (Use 3.14 for π.)
Container Shape Size Can Cylinder r = 5 cm, h = 7 cm Box Rectangular prism 6 cm × 8 cm × 9 cm - The can
- They hold the same amount
- The box
The can
Hint: Can: 3.14 × 5 × 5 × 7 = 549.5 cm³. Box: 6 × 8 × 9 = 432 cm³. The can holds more.
Question 4
A box has a volume of 120 cm³. It is 8 cm long and 3 cm wide. How tall is it?
answer boxcm
5 cm
Hint: V = l × w × h, so 120 = 8 × 3 × h = 24 × h. Divide: h = 120 ÷ 24 = 5 cm.
Question 5
A cube has edges 5 cm long. What is its volume?
- 25 cm³
- 125 cm³
- 150 cm³
- 60 cm³
125 cm³
Hint: All three dimensions are 5 cm: V = 5 × 5 × 5 = 125 cm³. (25 is the area of one face.)
Question 6
A box is 12 cm long, 8 cm wide and 3 cm high. What is its volume?
answer boxcm³
288 cm³
Hint: V = l × w × h = 12 × 8 × 3 = 96 × 3 = 288 cm³.