Grade 8 · Math · Unit 17 of 18
Surface Area & Volume
Prisms, cylinders, nets and views
What your child practises
Finding surface area and volume of boxes, cubes, triangular prisms and cylinders, working backwards to a missing dimension, linking cm³ to millilitres, and recognizing nets and views of 3D objects.
Ontario Curriculum expectation: E2.3 · surface area and volume of prisms and cylinders
How we explain it
Children can open this short lesson before they practise.
- 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
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 3 cm long, 5 cm wide and 9 cm tall. What is its surface area?
answer boxcm²
Show answer
174 cm²
Hint: Add the areas of the 3 pairs of faces: 2 × (3×5 + 3×9 + 5×9) = 2 × 87 = 174 cm².
Question 2
A cube has edges of 6 cm. What is its surface area?
answer boxcm²
Show answer
216 cm²
Hint: A cube has 6 identical square faces: 6 × 6² = 6 × 36 = 216 cm².
Question 3
A triangular prism has a triangle base of 14 cm and height 9 cm. The prism is 4 cm long. What is its volume?
answer boxcm³
Show answer
252 cm³
Hint: Area of the triangle = ½ × 14 × 9 = 63 cm². Volume = base area × length = 63 × 4 = 252 cm³.
Question 4
A cylinder has a radius of 4 cm and a height of 20 cm. What is its volume? Use π ≈ 3.14 and round to 1 decimal place.
answer boxcm³
Show answer
1004.8 cm³
Hint: V = π × r² × h ≈ 3.14 × 16 × 20 = 1004.8. Rounded: 1004.8 cm³.
Question 5
What is the surface area of a closed cylinder with radius 2 cm and height 15 cm? Use π ≈ 3.14 and round to 1 decimal place.
answer boxcm²
Show answer
213.5 cm²
Hint: SA = 2πr² + 2πrh = 2π × 2 × (2 + 15) ≈ 3.14 × 68 = 213.52. Rounded: 213.5 cm².
Question 6
A box with a volume of 60 cm³ is 2 cm long and 10 cm wide. How tall is it?
answer boxcm
Show answer
3 cm
Hint: Volume = l × w × h, so h = 60 ÷ (2 × 10) = 60 ÷ 20 = 3 cm.