You are the lead exhibit engineer for Coral Cove Aquarium. The director wants a brand-new ocean exhibit built from glass prism tanks and a glass pyramid skylight. Use volume to size the water, use nets to size the glass, estimate the cost and the water weight, and bring the build in under $90,000 without overloading the floor.
The director handed you a scaled exhibit plan. Every blueprint on this page uses the same scale:
SCALE 1 grid square = 1 foot · exhibit plan drawn to scale
Volume is how much space a solid fills, measured in cubic feet (ft³). Surface area is how much flat material covers the outside, measured in square feet (ft²). A net is the shape you get when you unfold a solid flat — every face becomes a piece you can measure.
Español: El volumen es cuánto espacio llena un sólido (pies cúbicos, ft³). El área de superficie es cuánto material cubre el exterior (pies cuadrados, ft²). Una red (net) es el sólido desdoblado en plano: cada cara es una pieza que puedes medir.Strategy — for volume, fill the solid with unit cubes. For surface area, unfold the solid into a net, find each flat face, then add them all up. Same solid, two different questions.
The centerpiece is a glass rectangular prism tank. Read its dimensions off the scale blueprint, then size the water it holds. Use the cube packer below to see how unit cubes fill the tank before you calculate. A low coral ledge runs along the back with a fractional height — size that too.
Build up to 18 × 8 × 6 one layer at a time. The volume equals the base layer (l × w) multiplied by the number of layers (h).
Q1.1 — Volume of the main tank (18 ft × 8 ft × 6 ft)
Q1.2 — The coral ledge is a smaller prism: 8 ft long, 3 ft wide, and only 1½ ft high. Find its volume. (Hint: 1½ = 1.5)
Volume of a box = length × width × height. Multiply two numbers first, then multiply by the third. For 1½, use 1.5.
Español: Volumen de una caja = largo × ancho × altura. Multiplica dos números y luego por el tercero. Para 1½ usa 1.5.Saltwater weighs about 62.4 lb per cubic foot. If the main tank is filled, about how many pounds of water sit on the floor? (864 × 62.4). Why does an engineer need to know that number before building?
A wedge-shaped viewing tunnel sits beside the reef. Its cross-section is a triangle, and it runs the full length of the wall — that makes it a triangular prism. Find the triangle base area first, then the volume.
Q2.1 — Area of the triangle cross-section (½ × 6 × 4)
Q2.2 — Volume of the wedge (base area × length, length = 10 ft)
Two steps. (1) Find the triangle area: ½ × base × height. (2) Multiply that area by how long the prism is.
Español: Dos pasos. (1) Área del triángulo: ½ × base × altura. (2) Multiplica esa área por el largo del prisma.A triangular prism holds half the water of the rectangular box that surrounds it (6 × 4 × 10 = 240 ft³). Does your answer match 240 ÷ 2? Explain why the triangle prism is exactly half.
Before the glass shop can cut panels, you must unfold the main tank into a net — every face becomes a flat panel. Click each panel on the net to mark it "counted," then add the areas to get the total glass surface area.
Q3.1 — How many panels (faces) does the tank net have? Click all of them on the diagram, then enter the count.
Q3.2 — Total glass surface area. Add the six panels: two 18×8 + two 18×6 + two 8×6.
A box has 3 pairs of matching faces: top & bottom, front & back, two ends. Find one of each, then double it, then add.
Español: Una caja tiene 3 pares de caras iguales: arriba y abajo, frente y atrás, dos extremos. Halla una de cada par, duplícala y suma todo.The real tank has no glass top (it is open for feeding). What surface area of glass do you actually order if you skip the top 18×8 panel? (600 − 144).
A glass square pyramid skylight crowns the exhibit. Its net is one square base plus four triangles. Find its surface area, choose a glass grade, then complete the Build Sheet under the $90,000 budget.
Q4.1 — Surface area of the pyramid skylight. Square base (6×6) plus four triangles (each ½ × 6 × 5).
Live glass cost = 600 ft² × price/ft². This feeds straight into your Build Sheet below.
| Item | Quantity | Your cost ($) |
|---|---|---|
| Tank glass — your grade | 600 ft² | |
| Pyramid skylight — low-iron @ $55/ft² | 96 ft² | |
| Saltwater fill — 864 + 120 ft³ @ $3/ft³ | 984 ft³ | |
| Pumps, frame & labor — fixed | — | |
| Total estimate | $0 |
Pyramid cost = 96 ft² × $55. Water cost = 984 ft³ × $3. Compute each and enter it to confirm you can turn area and volume into money.
If the acrylic grade ($70/ft²) pushes you over budget, what is the most expensive tank-glass price p you can still afford? Set up and solve the inequality:
600·p + 5280 + 2952 + 38000 ≤ 90000
Total = tank glass + pyramid + water + fixed. Remaining = budget − total. Positive remaining = under budget (good). Negative = pick a cheaper glass grade.
Español: Total = vidrio del tanque + pirámide + agua + fijo. Restante = presupuesto − total. Si es positivo, estás dentro del presupuesto.When every spec checks out and your plan is under budget, submit it to the aquarium director. Enter your name in the field below, then press Submit plan & grade to save your score as a PDF or DOC.
| Level | Score | Descriptor |
|---|---|---|
| 4 — Exceeds | 7 / 7 | Reads every scale blueprint accurately. Finds prism volumes (including a fractional edge) and triangular-prism volume correctly, uses nets to find surface area of a prism and a pyramid, and brings the build under budget. Can explain water weight and the glass-budget inequality. |
| 3 — Meets | 6 / 7 | Correctly computes most volumes and surface areas with at most one arithmetic slip. Completes the Build Sheet and reaches a valid under-budget plan. |
| 2 — Approaching | 4–5 / 7 | Computes simple volumes but struggles with the fractional edge, the triangular prism, or the net surface area (e.g., forgets to double matching faces or to halve the triangle). Partial cost/budget work. |
| 1 — Beginning | 0–3 / 7 | Few correct answers. Confuses volume with surface area, or misreads the scale. Needs reteaching on prism volume and on building surface area from a net. |