You are designing and building a custom fish tank. Use volume and surface area to figure out how much water it holds, how much glass is needed, and whether your budget can handle the build.
Your community center wants a custom rectangular fish tank. You must figure out its total volume, how much water it holds at a certain fill level, how much glass is needed (the tank is open at the top — no top face!), and whether the glass cost fits the budget. Work through all four phases, then write your build plan.
Find the total volume of the tank using V = l × w × h. This tells you the maximum amount the tank could hold if completely filled.
Multiply length × width to find how many unit cubes fit in one layer on the bottom of the tank. Then multiply by the height to count all the layers stacked up. For a 5 × 2 × 3 tank: 5 × 2 = 10 cubes per layer, 10 × 3 = 30 cubic units total.
Tanks are never filled all the way to the top. Use the same formula with a fill height (less than the full tank height) to find the volume of water actually in the tank.
Use the same V = l × w × h formula, but replace h with your fill height. For the 5 × 2 tank filled to 2 units: V = 5 × 2 × 2 = 20 cubic units of water. That is 20/30 (about 67%) of the full tank.
A fish tank is open at the top — there is no glass lid. So you only need glass for the bottom and the four sides. This is different from a closed box!
Compare open-top vs. closed box: a closed box with SA = 2(lw + lh + wh) has 6 faces. An open-top tank removes the top face (one l × w panel). So SAopen = 2(lw + lh + wh) − lw = lw + 2lh + 2wh. For a 5 × 2 × 3 tank: (5×2) + 2(5×3) + 2(2×3) = 10 + 30 + 12 = 52 square units.
Now that you know how many square units of glass are needed, multiply by the price per square unit to find the total glass cost for your tank.
Write a 3–5 sentence build plan using your real numbers. Describe the tank dimensions, its volume, the water volume at fill height, the glass area needed (open-top), and the total glass cost.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Volume (6.G.2) | Full and partial fill volumes both correct with unit labels; unit-cube reasoning explained | Both volume calculations correct | Formula applied but computation error |
| Partial Fill (6.G.2) | Fill height correctly substituted; fraction of full volume noted | Water volume correct | Formula used but incorrect fill height applied |
| Open-Top Surface Area (6.G.4) | 5-face net correctly identified; SA = lw + 2lh + 2wh applied; distinction from closed box explained | Open-top surface area correct | Used closed-box formula (included top face) or one face missing |
| Application / Communication | Glass cost correct; build plan justifies design with all numbers | Cost correct; build plan uses most numbers | Attempted; plan unclear or missing numbers |