Grade 9 · Math · Unit 9 of 10
Surface Area of Objects
Prisms, cylinders and joined shapes
What your child practises
Finding the surface area of a rectangular prism, of two solids joined together (taking away the faces that are hidden), and of a cylinder written in terms of π.
Alberta Curriculum learning outcome: SS2 · surface area of composite 3-D objects made from prisms and cylinders
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 cube with edges of 3 cm sits on top of a cube with edges of 5 cm, glued face to face. What is the surface area of the whole object, in cm²?
answer boxcm²
Show answer
186 cm²
Hint: Separately the cubes have 6 × 5² + 6 × 3² = 204 cm². Two faces of 3² = 9 cm² each are hidden where they touch: subtract 18.
Question 2
What is the surface area of a rectangular prism that is 10 cm long, 6 cm wide and 2 cm high, in cm²?
answer boxcm²
Show answer
184 cm²
Hint: Add the area of all 6 faces: 2 × (60 + 20 + 12) = 184.
Question 3
3 identical cubes are glued face to face in a straight row. How many cube faces can you see on the outside?
- 13
- 18
- 14
- 15
Show answer
14
Hint: 3 separate cubes have 18 faces. Each of the 2 glued joins hides 2 faces, so 18 − 4 = 14.
Question 4
Two rectangular prisms, 5 cm by 4 cm by 2 cm and 5 cm by 4 cm by 2 cm, are joined along their 4 cm by 2 cm faces. What is the surface area of the new object, in cm²?
answer boxcm²
Show answer
136 cm²
Hint: Add the two surface areas (76 + 76) and subtract the two hidden faces, 2 × 8 = 16.
Question 5
A closed cylinder has radius 4 cm and height 9 cm. What is its total surface area, in terms of π?
- 72π cm²
- 104π cm²
- 288π cm²
- 88π cm²
Show answer
104π cm²
Hint: Two circular ends: 2 × π × 4² = 32π. Curved side: 2π × 4 × 9 = 72π. Add them.
Question 6
A cylinder has radius 6 cm and height 7 cm. What is the area of its curved side, in terms of π?
- 42π cm²
- 84π cm²
- 120π cm²
- 156π cm²
Show answer
84π cm²
Hint: Unroll the curved side into a rectangle: its width is the circumference (2π × 6) and its height is 7. Area = 2π × 6 × 7 = 84π.