A maker club builds a glass aquarium. Volume (with fractional edges) and surface area decide the water capacity and how much glass to buy.
The club designed a tank 5 ft long, 2 ft wide, and 3 ft tall. The capacity is the volume.
V = l × w × h = 5 × 2 × 3 = 30 cubic feet.
Why is volume the right measure for how much water the tank holds?
A tank is 4 × 3 × 2 ft. Find its volume.
A divider shelf was thin: 1½ ft × 2 ft × 4 ft. The volume formula works the same with fractional edge lengths — just multiply carefully (1½ = 1.5).
V = 1.5 × 2 × 4 = 12 cubic feet.
Find the volume of a box 2½ × 2 × 4 ft. (2½ = 2.5)
Does the volume formula change when an edge is a fraction like 1½?
For a sealed display cube case, the club needed the surface area — the total area of all 6 faces. For a box, SA = 2(lw + lh + wh). The case was 2 × 3 × 4 ft.
SA = 2(lw + lh + wh) = 2(2·3 + 2·4 + 3·4) = 2(6 + 8 + 12) = 2(26) = 52 square feet.
Find the surface area of a closed box 2 × 2 × 5 ft. Use SA = 2(lw + lh + wh).
The real aquarium has no top — it is open so you can add water and fish. So the glass covers the bottom and the 4 sides, but not the top. For the 5 × 2 × 3 tank:
Glass = bottom + 4 sides = lw + 2(lh) + 2(wh) = 10 + 2(15) + 2(6) = 10 + 30 + 12 = 52 square feet. (A closed box would also count the top.)
An open-top tank is 4 × 2 × 3 ft. Glass = lw + 2lh + 2wh. How much glass (ft²)?
Why is the open-top tank's glass area less than a closed box of the same size?
Optional academic frame: "Volume measures ______, while surface area measures ______; for this tank that means ______."
Glass costs $3 per square foot. For the open-top 5 × 2 × 3 tank (52 ft² of glass), what is the glass cost? Then, if the club only fills the tank to a height of 2 ft, what volume of water is used? Explain each step. (Try it, then check with your teacher.)
| Category | 4 — Advanced | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Comprehension & inference | All analysis questions correct; distinguishes volume, SA, and open-top | 2 of 3 correct | 1 correct |
| Multi-step math | All 4 Solve-It answers correct (volume, fractional edge, closed SA, open-top glass) | 3 correct | 2 correct |
| Mathematical argument | Clear claim; distinguishes volume vs. SA with specific numbers | Claim with some evidence | Little evidence |
Grading accepts common formats (24, 24.0, "24 ft³").