7th grade · Math · Unit 10 of 22
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.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: 7.9(A) · volume of prisms
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 Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 10 of 22 in 7th grade Math, after Circles and before Nets & Surface Area.
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: Texas Education Agency (TEA)
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
Which container holds more? (Use 3.14 for π.)
Container Shape Size Can Cylinder r = 2 cm, h = 5 cm Box Rectangular prism 3 cm × 4 cm × 8 cm - The can
- They hold the same amount
- The box
The box
Hint: Can: 3.14 × 2 × 2 × 5 = 62.8 cm³. Box: 3 × 4 × 8 = 96 cm³. The box holds more.
Question 2
A box has a volume of 405 cm³. It is 9 cm long and 5 cm wide. How tall is it?
answer boxcm
9 cm
Hint: V = l × w × h, so 405 = 9 × 5 × h = 45 × h. Divide: h = 405 ÷ 45 = 9 cm.
Question 3
A cylinder's circular base has an area of 113.04 cm². The cylinder is 2 cm tall. What is its volume?
- 226.08 cm³
- 709.89 cm³
- 113.04 cm³
- 115.04 cm³
226.08 cm³
Hint: Volume = base area × height = 113.04 × 2 = 226.08 cm³. The base area already includes π, so don't multiply by 3.14 again.
Question 4
A cylinder has a radius of 7 cm and a height of 5 cm. What is its volume? Use 3.14 for π and round to one decimal place.
answer boxcm³
769.3 cm³
Hint: V = π × r × r × h ≈ 3.14 × 7 × 7 × 5 = 3.14 × 245 = 769.3. Rounded: 769.3 cm³.
Question 5
What does the volume of a container tell you?
- How far it is around the outside
- How much area its base covers
- How tall it is
- How much space is inside it
How much space is inside it
Hint: Volume measures the space a 3-D object takes up or holds, in cubic units.
Question 6
1000 cm³ holds 1 L. How many liters of water fill a fish tank 30 cm × 15 cm × 25 cm?
answer boxL
11.25 L
Hint: Volume: 30 × 15 × 25 = 11250 cm³. Divide by 1000 to change to liters: 11.25 L.