9th grade · Math · Unit 11 of 18
Surface Area of Objects
Prisms, cylinders and joined shapes
What your child practices
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.
Alabama Course of Study content standard: GDA.17 · surface area of prisms, cylinders and composite solids
How we explain it
Children can open this short lesson before they practice.
- Surface area is the total area of the outside faces.
- For a composite object, add the exposed faces only.
- 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
Surface Area of Objects in Alabama
In the Alabama Course of Study, this is unit 11 of 18 in 9th grade Math, after Line & Rotation Symmetry and before Volume & Units.
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 small cube is cut out of one corner of a larger cube. Compared with the original cube, the surface area is…
- impossible to tell
- larger
- the same
- smaller
the same
Hint: Three faces of the small cube are removed, but three new faces of the same size appear inside the notch. The surface area stays the same.
Question 2
A cylinder has radius 4 cm and height 11 cm. What is the area of its curved side, in terms of π?
- 44π cm²
- 88π cm²
- 120π cm²
- 104π cm²
88π cm²
Hint: Unroll the curved side into a rectangle: its width is the circumference (2π × 4) and its height is 11. Area = 2π × 4 × 11 = 88π.
Question 3
A cube with edges of 2 cm sits on top of a cube with edges of 3 cm, glued face to face. What is the surface area of the whole object, in cm²?
answer boxcm²
70 cm²
Hint: Separately the cubes have 6 × 3² + 6 × 2² = 78 cm². Two faces of 2² = 4 cm² each are hidden where they touch: subtract 8.
Question 4
5 identical cubes are glued face to face in a straight row. How many cube faces can you see on the outside?
- 30
- 21
- 22
- 23
22
Hint: 5 separate cubes have 30 faces. Each of the 4 glued joins hides 2 faces, so 30 − 8 = 22.
Question 5
A closed cylinder has radius 6 cm and height 4 cm. What is its total surface area, in terms of π?
- 120π cm²
- 48π cm²
- 84π cm²
- 288π cm²
120π cm²
Hint: Two circular ends: 2 × π × 6² = 72π. Curved side: 2π × 6 × 4 = 48π. Add them.
Question 6
A cube with edges of 2 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
166 cm²
Hint: Separately the cubes have 6 × 5² + 6 × 2² = 174 cm². Two faces of 2² = 4 cm² each are hidden where they touch: subtract 8.