Volume and surface area

Volume is base area times height, and that stays true with fractional edges: a 2½ × 1⅓ × 3 prism has volume 10. A net is the surface unfolded, so surface area is the sum of the face areas on the net. Students match nets to cubes, rectangular and triangular prisms, and square pyramids, and compute surface area from a net or from dimensions. Surface area of a non-cube box is not 6ℓw; it is 2(ℓw + ℓh + wh). A net whose faces would overlap when folded is not a valid net.

Specification · for a parent or teacher
Part no.
volume-surface-nets
Course
Advanced Math 6 · Unit 12
Also in
High School Math 1
Realm
Shapes
Difficulty
3 of 4 Grade 6–7 core. Multi-step, first symbolic work.
Qty
5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

V=wh=BhV=\ell wh = Bh with fractional edges; match nets to cubes, rectangular and triangular prisms, square pyramids; compute surface area from a net.

Ready when

VV of a 212×113×32\frac12 \times 1\frac13 \times 3 prism, and surface area of a given net, both correct.

Formulas

Prism volume
V=wh=BhV = \ell w h = B h
Box surface area
S=2(w+h+wh)S = 2(\ell w + \ell h + w h)
Cube surface area
S=6s2S = 6 s^2

Watch for

surface area as 6w6\ell w for a non-cube; a net that folds into overlapping faces accepted as valid.

Before · requires

After · used by

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volume-surface-nets

Items: volume-surface-nets-01 · volume-surface-nets-02 · volume-surface-nets-03 · volume-surface-nets-04 · volume-surface-nets-05