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.
Alaska content standards learning standard: 8.G.9 · volume of cylinders
How we explain it
Children can open this short lesson before they practice.
- Surface area is the area of all the faces added up.
- Volume of a cylinder: V = π × r² × h.
- 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 Alaska
In the Alaska content standards, 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: 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 box is 7 cm long, 9 cm wide and 6 cm tall. What is its surface area?
answer boxcm²
318 cm²
Hint: Add the areas of the 3 pairs of faces: 2 × (7×9 + 7×6 + 9×6) = 2 × 159 = 318 cm².
Question 2
A cube has edges of 9 cm. What is its surface area?
answer boxcm²
486 cm²
Hint: A cube has 6 identical square faces: 6 × 9² = 6 × 81 = 486 cm².
Question 3
A triangular prism has a triangle base of 8 cm and height 6 cm. The prism is 11 cm long. What is its volume?
answer boxcm³
264 cm³
Hint: Area of the triangle = ½ × 8 × 6 = 24 cm². Volume = base area × length = 24 × 11 = 264 cm³.
Question 4
A cylinder has a radius of 4 cm and a height of 10 cm. What is its volume? Use π ≈ 3.14 and round to 1 decimal place.
answer boxcm³
502.4 cm³
Hint: V = π × r² × h ≈ 3.14 × 16 × 10 = 502.4. Rounded: 502.4 cm³.
Question 5
What is the surface area of a closed cylinder with radius 6 cm and height 5 cm? Use π ≈ 3.14 and round to 1 decimal place.
answer boxcm²
414.5 cm²
Hint: SA = 2πr² + 2πrh = 2π × 6 × (6 + 5) ≈ 3.14 × 132 = 414.48. Rounded: 414.5 cm².
Question 6
A box with a volume of 144 cm³ is 3 cm long and 8 cm wide. How tall is it?
answer boxcm
6 cm
Hint: Volume = l × w × h, so h = 144 ÷ (3 × 8) = 144 ÷ 24 = 6 cm.