8th grade · Math · Unit 4 of 19
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.
New York State Learning Standards learning standard: NY-8.G.9 · the 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 New York
In the New York State Learning Standards, this is unit 4 of 19 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.
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 8 cm long, 4 cm wide and 4 cm tall. What is its surface area?
answer boxcm²
160 cm²
Hint: Add the areas of the 3 pairs of faces: 2 × (8×4 + 8×4 + 4×4) = 2 × 80 = 160 cm².
Question 2
A cube has edges of 3 cm. What is its surface area?
answer boxcm²
54 cm²
Hint: A cube has 6 identical square faces: 6 × 3² = 6 × 9 = 54 cm².
Question 3
A triangular prism has a triangle base of 14 cm and height 10 cm. The prism is 12 cm long. What is its volume?
answer boxcm³
840 cm³
Hint: Area of the triangle = ½ × 14 × 10 = 70 cm². Volume = base area × length = 70 × 12 = 840 cm³.
Question 4
A cylinder has a radius of 3 cm and a height of 3 cm. What is its volume? Use π ≈ 3.14 and round to 1 decimal place.
answer boxcm³
84.8 cm³
Hint: V = π × r² × h ≈ 3.14 × 9 × 3 = 84.78. Rounded: 84.8 cm³.
Question 5
What is the surface area of a closed cylinder with radius 4 cm and height 13 cm? Use π ≈ 3.14 and round to 1 decimal place.
answer boxcm²
427.0 cm²
Hint: SA = 2πr² + 2πrh = 2π × 4 × (4 + 13) ≈ 3.14 × 136 = 427.04. Rounded: 427.0 cm².
Question 6
A box with a volume of 90 cm³ is 3 cm long and 5 cm wide. How tall is it?
answer boxcm
6 cm
Hint: Volume = l × w × h, so h = 90 ÷ (3 × 5) = 90 ÷ 15 = 6 cm.