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Aquarium Volume worksheet

Grades 7–8 · CCSS 7.G.B.6, 8.G.C.9

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Tank shape: Cylinder
- Measurements in: Centimeters
- Diameter: 16
- Height: 13
- Glass thickness: 0
- Water level below the top: 2
- Water: Saltwater (1.025)
Find: Water volume
Answer
2.
Problem 2.
- Tank shape: Rectangular
- Measurements in: Inches
- Length (left to right): 26
- Width (front to back): 8
- Height: 15
- Glass thickness: 0
- Water level below the top: 1
- Water: Freshwater
Find: Water volume
Answer
3.
Problem 3.
- Tank shape: Hexagon
- Measurements in: Centimeters
- Width across opposite flat sides: 23
- Height: 15
- Glass thickness: 0
- Water level below the top: 1
- Water: Saltwater (1.025)
Find: Water volume
Answer
4.
Problem 4.
- Tank shape: Hexagon
- Measurements in: Inches
- Width across opposite flat sides: 14
- Height: 12
- Glass thickness: 0
- Water level below the top: 1
- Water: Saltwater (1.025)
Find: Water volume
Answer
5.
Problem 5.
- Tank shape: Rectangular
- Measurements in: Inches
- Length (left to right): 26
- Width (front to back): 8
- Height: 13
- Glass thickness: 0
- Water level below the top: 1
- Water: Saltwater (1.025)
Find: Water volume
Answer
6.
Problem 6.
- Tank shape: Cylinder
- Measurements in: Centimeters
- Diameter: 15
- Height: 15
- Glass thickness: 0
- Water level below the top: 1
- Water: Saltwater (1.025)
Find: Water volume
Answer
7.
Problem 7.
- Tank shape: Hexagon
- Measurements in: Inches
- Width across opposite flat sides: 18
- Height: 15
- Glass thickness: 0
- Water level below the top: 1
- Water: Freshwater
Find: Water volume
Answer
8.
Problem 8.
- Tank shape: Cylinder
- Measurements in: Inches
- Diameter: 22
- Height: 10
- Glass thickness: 0
- Water level below the top: 1
- Water: Freshwater
Find: Water volume
Answer
9.
Problem 9.
- Tank shape: Hexagon
- Measurements in: Centimeters
- Width across opposite flat sides: 18
- Height: 13
- Glass thickness: 0
- Water level below the top: 1
- Water: Freshwater
Find: Water volume
Answer
10.
Problem 10.
- Tank shape: Cylinder
- Measurements in: Centimeters
- Diameter: 17
- Height: 15
- Glass thickness: 0
- Water level below the top: 1
- Water: Saltwater (1.025)
Find: Water volume
Answer

Answer key: Aquarium Volume worksheet

1. Water volume: 2.2 L
1. Inside floor area = π × (inside diameter ÷ 2)²
  $π \times {(\frac{16}{2})}^{2}$ $= 201.0619 cm²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $13 - 0 - 2$ $= 11 cm$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $201.0619 \times 11$ $= 2,211.6812 cm³$
4. Convert to liters (1 L = 1,000 cm³)
  $\frac{2,211.6812}{1,000}$ $= 2.211681 L$
5. Find how much the water weighs: liters × 1.025 kg per liter
  $2.2117 \times 1.025$ $= 2.267 kg$
2. Water volume: 12.6 US gal
1. Find the inside floor area. Take the glass off both ends and both sides: (length − 2 × glass) × (width − 2 × glass)
  $26 in \times 8 in$ $= 208 in²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $15 - 0 - 1$ $= 14 in$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $208 \times 14$ $= 2,912 in³$
4. Convert to US gallons (1 gal = 231 in³)
  $\frac{2,912}{231}$ $= 12.606061 US gal$
5. Find how much the water weighs: liters × 1 kg per liter
  $47.7191 \times 1$ $= 47.7191 kg$
3. Water volume: 6.4 L
1. Inside floor area of a regular hexagon = (√3 ÷ 2) × (width across flats)²
  $\frac{\sqrt{3}}{2} \times 23^{2}$ $= 458.1274 cm²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $15 - 0 - 1$ $= 14 cm$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $458.1274 \times 14$ $= 6,413.7841 cm³$
4. Convert to liters (1 L = 1,000 cm³)
  $\frac{6,413.7841}{1,000}$ $= 6.413784 L$
5. Find how much the water weighs: liters × 1.025 kg per liter
  $6.4138 \times 1.025$ $= 6.5741 kg$
4. Water volume: 8.1 US gal
1. Inside floor area of a regular hexagon = (√3 ÷ 2) × (width across flats)²
  $\frac{\sqrt{3}}{2} \times 14^{2}$ $= 169.741 in²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $12 - 0 - 1$ $= 11 in$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $169.741 \times 11$ $= 1,867.1508 in³$
4. Convert to US gallons (1 gal = 231 in³)
  $\frac{1,867.1508}{231}$ $= 8.082904 US gal$
5. Find how much the water weighs: liters × 1.025 kg per liter
  $30.5971 \times 1.025$ $= 31.362 kg$
5. Water volume: 10.8 US gal
1. Find the inside floor area. Take the glass off both ends and both sides: (length − 2 × glass) × (width − 2 × glass)
  $26 in \times 8 in$ $= 208 in²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $13 - 0 - 1$ $= 12 in$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $208 \times 12$ $= 2,496 in³$
4. Convert to US gallons (1 gal = 231 in³)
  $\frac{2,496}{231}$ $= 10.805195 US gal$
5. Find how much the water weighs: liters × 1.025 kg per liter
  $40.9021 \times 1.025$ $= 41.9247 kg$
6. Water volume: 2.5 L
1. Inside floor area = π × (inside diameter ÷ 2)²
  $π \times {(\frac{15}{2})}^{2}$ $= 176.7146 cm²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $15 - 0 - 1$ $= 14 cm$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $176.7146 \times 14$ $= 2,474.0042 cm³$
4. Convert to liters (1 L = 1,000 cm³)
  $\frac{2,474.0042}{1,000}$ $= 2.474004 L$
5. Find how much the water weighs: liters × 1.025 kg per liter
  $2.474 \times 1.025$ $= 2.5359 kg$
7. Water volume: 17 US gal
1. Inside floor area of a regular hexagon = (√3 ÷ 2) × (width across flats)²
  $\frac{\sqrt{3}}{2} \times 18^{2}$ $= 280.5922 in²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $15 - 0 - 1$ $= 14 in$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $280.5922 \times 14$ $= 3,928.2912 in³$
4. Convert to US gallons (1 gal = 231 in³)
  $\frac{3,928.2912}{231}$ $= 17.00559 US gal$
5. Find how much the water weighs: liters × 1 kg per liter
  $64.3732 \times 1$ $= 64.3732 kg$
8. Water volume: 14.8 US gal
1. Inside floor area = π × (inside diameter ÷ 2)²
  $π \times {(\frac{22}{2})}^{2}$ $= 380.1327 in²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $10 - 0 - 1$ $= 9 in$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $380.1327 \times 9$ $= 3,421.1944 in³$
4. Convert to US gallons (1 gal = 231 in³)
  $\frac{3,421.1944}{231}$ $= 14.810365 US gal$
5. Find how much the water weighs: liters × 1 kg per liter
  $56.0633 \times 1$ $= 56.0633 kg$
9. Water volume: 3.4 L
1. Inside floor area of a regular hexagon = (√3 ÷ 2) × (width across flats)²
  $\frac{\sqrt{3}}{2} \times 18^{2}$ $= 280.5922 cm²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $13 - 0 - 1$ $= 12 cm$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $280.5922 \times 12$ $= 3,367.1068 cm³$
4. Convert to liters (1 L = 1,000 cm³)
  $\frac{3,367.1068}{1,000}$ $= 3.367107 L$
5. Find how much the water weighs: liters × 1 kg per liter
  $3.3671 \times 1$ $= 3.3671 kg$
10. Water volume: 3.2 L
1. Inside floor area = π × (inside diameter ÷ 2)²
  $π \times {(\frac{17}{2})}^{2}$ $= 226.9801 cm²$
2. Find how deep the water is: the height, minus the bottom glass and the gap left below the top
  $15 - 0 - 1$ $= 14 cm$
3. Multiply the floor area by the water depth to get the volume of water, since the sides go straight up
  $226.9801 \times 14$ $= 3,177.721 cm³$
4. Convert to liters (1 L = 1,000 cm³)
  $\frac{3,177.721}{1,000}$ $= 3.177721 L$
5. Find how much the water weighs: liters × 1.025 kg per liter
  $3.1777 \times 1.025$ $= 3.2572 kg$