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Grade 9 · Math · Unit 8 of 9

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.

Prince Edward Island Curriculum curriculum outcome: 9.SS2 · surface area of prisms, cylinders and joined (composite) objects

How we explain it

Children can open this short lesson before they practise.

  1. Surface area is the total area of the outside faces.
  2. For a composite object, add the exposed faces only.
  3. Faces that join are no longer outside, so leave them out.

Example: Find the surface area of a cube with 2 cm edges. One face: 2 × 2 = 4 cm². 6 faces: 6 × 4 = 24. Answer: 24 cm²

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

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