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8th grade · Math · Unit 4 of 17

Surface Area & Volume

Prisms, cylinders, nets and views

What your child practices

Finding surface area and volume of boxes, cubes, triangular prisms and cylinders, working backwards to a missing dimension, linking cm³ to milliliters, and recognizing nets and views of 3D objects.

Alabama Course of Study content standard: 8.30 · volume of cylinders

How we explain it

Children can open this short lesson before they practice.

  1. Surface area is the area of all the faces added up.
  2. Volume of a cylinder: V = π × r² × h.
  3. Use π ≈ 3.14.

Example: A cylinder has radius 3 cm and height 5 cm. What is its volume? r² = 3 × 3 = 9. V ≈ 3.14 × 9 × 5 = 141.3. Answer: About 141.3 cm³

Surface Area & Volume in Alabama

In the Alabama Course of Study, this is unit 4 of 17 in 8th grade Math, after Pythagorean Theorem and before Big, Small & Real Numbers.

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: Alabama State Department of Education (ALSDE)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A box is 10 cm long, 4 cm wide and 5 cm tall. What is its surface area?

    answer boxcm²

  2. Question 2

    A cube has edges of 9 cm. What is its surface area?

    answer boxcm²

  3. Question 3

    A triangular prism has a triangle base of 6 cm and height 10 cm. The prism is 11 cm long. What is its volume?

    answer boxcm³

  4. Question 4

    A cylinder has a radius of 6 cm and a height of 6 cm. What is its volume? Use π ≈ 3.14 and round to 1 decimal place.

    answer boxcm³

  5. Question 5

    What is the surface area of a closed cylinder with radius 8 cm and height 16 cm? Use π ≈ 3.14 and round to 1 decimal place.

    answer boxcm²

  6. Question 6

    A box with a volume of 336 cm³ is 6 cm long and 7 cm wide. How tall is it?

    answer boxcm

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