Surface area and volume of solids
Solve real-world and mathematical problems involving the surface area and volume of right prisms (including triangular and trapezoidal prisms) and of solids composed of cubes and right prisms: find a prism's surface area as the two bases plus the rectangular side faces; find volume as base area × height, including bases that are composite polygons; for composite solids, add the volumes of the parts but find the surface area from the exposed faces only, subtracting the areas hidden where parts join; and decide whether a problem needs area, surface area or volume
Lesson
Set out your lesson
“Surface area and volume of solids means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Unit cubes or squared paper nets
- Pencil for recording
Extra for the adult
Worked example. A 2 by 3 by 4 cuboid has volume 24 unit cubes.
Optional challenge. For Surface area and volume of solids, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Surface area and volume of solids, not mastery.
Share and support
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceSurface area and volume of solids practice
Practice key ideas from Surface area and volume of solids.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
Before you open · source notes
Area Builder supports hands-on exploration for Surface area and volume of solids. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Find the surface area of a triangular prism 10 cm long with right-triangle ends (sides 3 cm, 4 cm and 5 cm) as 2 × 6 + (3 + 4 + 5) × 10 = 132 cm²
- Find the volume (40 cm³) and surface area (80 cm², not 88 cm²) of a 2 cm cube glued on top of a 4 cm × 4 cm × 2 cm block, removing the two 4 cm² faces hidden where they join
- Find the soil for a planter 0.5 m deep whose L-shaped base is a 3 m × 1 m and a 2 m × 1.5 m rectangle (6 m² × 0.5 m = 3 m³), and explain why painting its outside walls needs surface area instead
“If your child built a model from two boxes glued together, could they work out how much space it takes up and how much paint would cover its outside — remembering not to paint the faces that are glued together?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 12–13
Standards