Phase 1 of 5

Mission Briefing

Welcome, Architect! The city aquarium needs your geometry skills to design brand-new marine exhibits.

Architect Registration

Enter your details to begin designing your aquarium.

Architect Name

Design Team (Class Period)

Project Date

Your Mission

The city aquarium is expanding! As the lead Architect, you must design tanks for different marine habitats. Use volume, surface area, and 3D geometry to create the perfect environments for each species.

Skills You'll Use:

Volume of rectangular prisms (V = L × W × H)
Surface area of rectangular prisms
Nets of 3D shapes
Unit conversions (cubic inches to gallons)
Comparing volumes and dimensions

Aquarium Design Guide:

🐠 Tropical Fish need at least 20 gallons
🦈 Seahorses need tall, narrow tanks
🐙 Sharks need at least 200 gallons
🌊 1 gallon ≈ 231 cubic inches
📏 Glass is measured by surface area

Level 1 Support — Key Vocabulary:

Volume = the amount of space inside a 3D shape, measured in cubic units
Rectangular prism = a 3D box shape with 6 flat faces (like a fish tank)
Surface area = the total area of all the outside faces added together
Net = a flat pattern that folds up into a 3D shape
Dimensions = the length, width, and height measurements
Cubic inches (in³) = a unit for measuring volume

Phase 2 of 5

Marine Research

Study 3D shapes, learn volume formulas, and explore how tanks are built.

3D Tank Volume Calculator

Adjust the length, width, and height to see the volume change in real time!

Length (in) 12

Width (in) 8

Height (in) 10

Volume = 12 × 8 × 10 = 960 in³

Water capacity ≈ 4.16 gallons

Volume formula: Volume = Length × Width × Height. Multiply all three numbers together. The answer is in cubic units (like in³). To convert to gallons: divide by 231.

Volume of Rectangular Prisms

Calculate the volume for each aquarium tank.

Clownfish Tank: L = 24 in, W = 12 in, H = 16 in. Volume = ?

Seahorse Column: L = 10 in, W = 10 in, H = 30 in. Volume = ?

Coral Display: L = 36 in, W = 18 in, H = 20 in. Volume = ?

Which tank holds the most water? Explain how you know.

Volume = L × W × H. Multiply all three dimensions. Compare the results to find the largest.

Gallons Conversion

Convert each tank's volume from cubic inches to gallons. (1 gallon ≈ 231 in³)

Clownfish Tank (your answer from Task 1) ÷ 231 = ? gallons

Seahorse Column ÷ 231 = ? gallons

Coral Display ÷ 231 = ? gallons

Which tanks have enough water for tropical fish (at least 20 gallons)?

Take the volume in cubic inches and divide by 231. Round to the nearest tenth. Then compare to 20 gallons.

Identifying Faces, Edges, and Vertices

A rectangular prism (fish tank) has specific geometric features. Identify them.

How many faces does a rectangular prism have?

How many edges does a rectangular prism have?

How many vertices (corners) does a rectangular prism have?

Which faces are identical (same size)? Describe the pairs.

A rectangular prism has 6 faces (3 pairs of identical rectangles), 12 edges (3 groups of 4 equal edges), and 8 vertices (corners).

Comparing Tank Shapes

Two tanks have the same volume but different shapes. Investigate!

Tank A: 20 in × 10 in × 12 in
Tank B: 15 in × 16 in × 10 in

Volume of Tank A:

Volume of Tank B:

Are the volumes equal? Which tank would be better for seahorses (they prefer taller tanks)? Why?

Calculate both volumes using V = L × W × H. Seahorses swim vertically, so look at which tank has the greater height.

Phase 3 of 5

Tank Planning

Calculate surface area for glass, explore nets, and plan your exhibit layouts.

Surface Area Calculator

Calculate how much glass is needed to build a tank (surface area of a rectangular prism).

📏 Glass Needed Calculator

Length: Width: Height:

Enter L, W, H and click Calculate.

Surface Area formula: SA = 2(L×W) + 2(L×H) + 2(W×H). This adds up the area of all 6 faces. For an open-top tank: SA = L×W + 2(L×H) + 2(W×H).

Water Volume Converter

Convert between different volume units for your tank designs.

🌊 Unit Converter

→

Enter a value and click Convert.

Surface Area for Glass

Calculate how much glass is needed (surface area) for each tank. Assume tanks have all 6 faces.

Mini Display: L = 12 in, W = 8 in, H = 10 in. Surface Area = ?

Show your work for the Mini Display calculation:

Large Reef Tank: L = 36 in, W = 18 in, H = 24 in. Surface Area = ?

Challenge: The large tank is open on top (no lid). How much glass is needed now? What is the difference?

SA = 2(L×W) + 2(L×H) + 2(W×H). Calculate each pair of faces separately, then add them all together.

Nets of Rectangular Prisms

A net is the flat pattern that folds into a 3D shape. Study the net below and answer the questions.

How many rectangles are in the net of a rectangular prism?

If L = 10 in, W = 6 in, H = 8 in, what is the area of the FRONT face?

What is the area of the RIGHT face?

What is the total surface area using the net? (Add all 6 face areas)

Find each face area: Top/Bottom = 10×6 = 60. Front/Back = 10×8 = 80. Left/Right = 6×8 = 48. Total = 2(60) + 2(80) + 2(48).

Design a Tank for a Specific Fish

A clownfish needs at least 20 gallons (4,620 in³). Design a tank that meets this requirement!

Your tank Length (in):

Your tank Width (in):

Your tank Height (in):

Calculate: Volume = L × W × H = ? in³

Is your volume at least 4,620 in³? How many gallons is it?

Challenge: What is the minimum height if L = 24 in and W = 12 in? Show your algebra.

Pick reasonable dimensions (like L=24, W=12, H=18). Multiply them together and check if the result is at least 4,620. If not, increase a dimension.

Phase 4 of 5

Aquarium Build

Design complete exhibits, solve real-world tank problems, and build your aquarium layout.

Glass Cost Calculation

Glass costs $0.05 per square inch. Calculate the glass cost for each tank (open-top, no lid).

Open-top SA formula: Bottom + 2(Front/Back) + 2(Left/Right) = (L×W) + 2(L×H) + 2(W×H)

Small Tank: L=18, W=10, H=12. Open-top SA = ?

Glass cost for Small Tank (SA × $0.05) = ?

Large Tank: L=48, W=24, H=20. Open-top SA = ?

Glass cost for Large Tank = ?

Open-top SA = (L×W) + 2(L×H) + 2(W×H). For the small tank: 180 + 432 + 240 = 852 in². Then 852 × $0.05 = $42.60.

Fill Time Challenge

A water hose fills at a rate of 3 gallons per minute. How long to fill each tank?

Tank holding 30 gallons: Time = ? minutes

Tank holding 55 gallons: Time = ? minutes

Giant display tank holding 200 gallons: Time = ? minutes. Convert to hours and minutes.

Challenge: If two hoses work together (3 gal/min each), how long for the 200-gallon tank? Show the math.

Time = Volume ÷ Rate. For 200 ÷ 3 = 66.67 minutes. That is 1 hour and about 7 minutes.

Design a Multi-Tank Exhibit

Design a 3-tank exhibit for the aquarium. Each tank must house a different species with specific volume requirements.

Species Requirements:
🐠 Tropical Fish: minimum 20 gallons (4,620 in³)
🦈 Seahorses: minimum 15 gallons (3,465 in³), height must be ≥ 20 in
🐙 Small Shark: minimum 100 gallons (23,100 in³)

Tropical Fish Tank — Dimensions (L × W × H) and Volume:

Seahorse Tank — Dimensions (L × W × H) and Volume:

Small Shark Tank — Dimensions (L × W × H) and Volume:

Total water needed for all 3 tanks combined (in gallons):

Volume Doubling Investigation

Explore what happens to volume when you change dimensions.

Original tank: L=10, W=8, H=6. Volume = ?

Double ONLY the length (L=20, W=8, H=6). New volume = ?

Double ALL dimensions (L=20, W=16, H=12). New volume = ?

When you double one dimension, the volume ___. When you double ALL dimensions, the volume ___. Explain the pattern.

Original: 480. Doubled length: 960 (2× original). All doubled: 3,840 (8× original). When you double all 3, you multiply by 2×2×2 = 8!

Exhibit Floor Plan

The aquarium has a room that is 120 inches long and 96 inches wide. Plan where to place your 3 tanks from Task 10.

Calculate the floor area of the room (L × W):

Calculate the floor footprint of each tank (L × W only). List all three:

Total floor space used by all 3 tanks:

What percentage of the room floor do the tanks cover?

Challenge: If you need 18 inches of walking space between tanks and walls, can all 3 tanks fit? Show your reasoning.

Room area = 120 × 96 = 11,520 in². For percentage: (total tank floor area ÷ 11,520) × 100.

Composite Shape Tanks

Some exhibits combine two rectangular prisms into one L-shaped tank. Calculate the total volume!

Volume of Section A (20 × 8 × 12):

Volume of Section B (10 × 10 × 12):

Total volume of the L-shaped tank:

Convert total to gallons:

Break the L-shape into two rectangular prisms. Find each volume, then add them together. Section A: 20×8×12 = 1,920. Section B: 10×10×12 = 1,200.

Aquarium Budget Planner

You have a $500 budget for materials. Plan your aquarium build!

Material Costs:
Glass: $0.05 per in² • Silicone sealant: $8 per tank • Gravel: $0.02 per in³ of tank volume • Water treatment: $3 per 10 gallons

Choose tank dimensions and calculate total glass cost (open-top SA × $0.05):

Gravel cost (volume of 2-inch gravel layer = L × W × 2, times $0.02):

Water treatment cost (gallons ÷ 10 × $3):

Total cost (Glass + Silicone + Gravel + Water treatment):

Are you under the $500 budget? How much money is left?