8th grade · Math · Unit 10 of 15
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.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.7(B) · lateral and total surface area of prisms and 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 Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 10 of 15 in 8th grade Math, after Cones, Cylinders & Spheres and before Pythagorean Theorem.
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
A box is 8 cm long, 6 cm wide and 8 cm tall. What is its surface area?
answer boxcm²
320 cm²
Hint: Add the areas of the 3 pairs of faces: 2 × (8×6 + 8×8 + 6×8) = 2 × 160 = 320 cm².
Question 2
A cube has edges of 10 cm. What is its surface area?
answer boxcm²
600 cm²
Hint: A cube has 6 identical square faces: 6 × 10² = 6 × 100 = 600 cm².
Question 3
A triangular prism has a triangle base of 6 cm and height 9 cm. The prism is 13 cm long. What is its volume?
answer boxcm³
351 cm³
Hint: Area of the triangle = ½ × 6 × 9 = 27 cm². Volume = base area × length = 27 × 13 = 351 cm³.
Question 4
A cylinder has a radius of 7 cm and a height of 17 cm. What is its volume? Use π ≈ 3.14 and round to 1 decimal place.
answer boxcm³
2615.6 cm³
Hint: V = π × r² × h ≈ 3.14 × 49 × 17 = 2615.62. Rounded: 2615.6 cm³.
Question 5
What is the surface area of a closed cylinder with radius 4 cm and height 19 cm? Use π ≈ 3.14 and round to 1 decimal place.
answer boxcm²
577.8 cm²
Hint: SA = 2πr² + 2πrh = 2π × 4 × (4 + 19) ≈ 3.14 × 184 = 577.76. Rounded: 577.8 cm².
Question 6
A box with a volume of 240 cm³ is 8 cm long and 3 cm wide. How tall is it?
answer boxcm
10 cm
Hint: Volume = l × w × h, so h = 240 ÷ (8 × 3) = 240 ÷ 24 = 10 cm.