Tank Volume worksheet

1. Liquid in the tank: 493.71 US gal

1. Total volume = length × width × height

   $11\times 3\times 5$$=165\text{\hspace{0.17em}ft³}$

2. Filled volume = length × width × liquid depth

   $11\times 3\times 2$$=66\text{\hspace{0.17em}ft³}$

3. Convert the filled volume to liters (1 ft³ = 28.31684659 L)

   $66\times 28.31684659$$=\mathrm{1,868.911875}\text{\hspace{0.17em}L}$

4. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{\mathrm{1,868.911875}}{3.785411784}$$=493.714286\text{\hspace{0.17em}US gal}$

2. Liquid in the tank: 0.17 US gal

1. Total volume = length × width × height

   $10\times 2\times 6$$=120\text{\hspace{0.17em}in³}$

2. Filled volume = length × width × liquid depth

   $10\times 2\times 2$$=40\text{\hspace{0.17em}in³}$

3. Convert the filled volume to liters (1 in³ = 0.01638706 L)

   $40\times 0.01638706$$=0.655483\text{\hspace{0.17em}L}$

4. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{0.655483}{3.785411784}$$=0.17316\text{\hspace{0.17em}US gal}$

3. Liquid in the tank: 0.05 L

1. Total volume = π × radius² × height

   $\pi \times 2^2\times 9$$=113.097336\text{\hspace{0.17em}cm³}$

2. Filled volume = π × radius² × liquid depth

   $\pi \times 2^2\times 4$$=50.265482\text{\hspace{0.17em}cm³}$

3. Convert the filled volume to liters (1 cm³ = 0.001 L)

   $50.265482\times 0.001$$=0.050265\text{\hspace{0.17em}L}$

4. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{0.050265}{3.785411784}$$=0.013279\text{\hspace{0.17em}US gal}$

4. Liquid in the tank: 0.18 US gal

1. Total volume = 4/3 × π × radius³

   $\frac{4}{3}\times \pi \times {2.5}^3$$=65.449847\text{\hspace{0.17em}in³}$

2. The liquid forms a rounded cap. Its volume, using radius r and depth h, is π × h² × (3r − h) ÷ 3

   $\frac{\pi \times 3^2\times \left(3\times 2.5-3\right)}{3}$$=42.411501\text{\hspace{0.17em}in³}$

3. Convert the filled volume to liters (1 in³ = 0.01638706 L)

   $42.411501\times 0.01638706$$=0.695\text{\hspace{0.17em}L}$

4. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{0.695}{3.785411784}$$=0.1836\text{\hspace{0.17em}US gal}$

5. Liquid in the tank: 105.75 US gal

1. Total volume = 4/3 × π × radius³

   $\frac{4}{3}\times \pi \times {1.5}^3$$=14.137167\text{\hspace{0.17em}ft³}$

2. The liquid forms a rounded cap. Its volume, using radius r and depth h, is π × h² × (3r − h) ÷ 3

   $\frac{\pi \times 3^2\times \left(3\times 1.5-3\right)}{3}$$=14.137167\text{\hspace{0.17em}ft³}$

3. Convert the filled volume to liters (1 ft³ = 28.31684659 L)

   $14.137167\times 28.31684659$$=400.319988\text{\hspace{0.17em}L}$

4. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{400.319988}{3.785411784}$$=105.753353\text{\hspace{0.17em}US gal}$

6. Liquid in the tank: 0.01 L

1. Total volume = 4/3 × π × radius³

   $\frac{4}{3}\times \pi \times {1.5}^3$$=14.137167\text{\hspace{0.17em}cm³}$

2. The liquid forms a rounded cap. Its volume, using radius r and depth h, is π × h² × (3r − h) ÷ 3

   $\frac{\pi \times 3^2\times \left(3\times 1.5-3\right)}{3}$$=14.137167\text{\hspace{0.17em}cm³}$

3. Convert the filled volume to liters (1 cm³ = 0.001 L)

   $14.137167\times 0.001$$=0.014137\text{\hspace{0.17em}L}$

4. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{0.014137}{3.785411784}$$=0.003735\text{\hspace{0.17em}US gal}$

7. Liquid in the tank: 370.14 US gal

1. Total volume = π × radius² × length

   $\pi \times {1.5}^2\times 7$$=49.480084\text{\hspace{0.17em}ft³}$

2. Seen from the end, the liquid fills a slice of the circle (a circular segment). Its area, using radius r and depth h, is r² × arccos((r − h) ÷ r) − (r − h) × √(2rh − h²)

   ${1.5}^2\times \text{arccos}\left(\frac{1.5-3}{1.5}\right)-\left(1.5-3\right)\times \sqrt{2\times 1.5\times 3-3^2}$$=7.068583\text{\hspace{0.17em}ft²}$

3. Filled volume = that slice's area × the tank length

   $7.068583\times 7$$=49.480084\text{\hspace{0.17em}ft³}$

4. Convert the filled volume to liters (1 ft³ = 28.31684659 L)

   $49.480084\times 28.31684659$$=\mathrm{1,401.119956}\text{\hspace{0.17em}L}$

5. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{\mathrm{1,401.119956}}{3.785411784}$$=370.136734\text{\hspace{0.17em}US gal}$

8. Liquid in the tank: 0.09 L

1. Total volume = π × radius² × length

   $\pi \times 2^2\times 7$$=87.964594\text{\hspace{0.17em}cm³}$

2. Seen from the end, the liquid fills a slice of the circle (a circular segment). Its area, using radius r and depth h, is r² × arccos((r − h) ÷ r) − (r − h) × √(2rh − h²)

   $2^2\times \text{arccos}\left(\frac{2-4}{2}\right)-\left(2-4\right)\times \sqrt{2\times 2\times 4-4^2}$$=12.566371\text{\hspace{0.17em}cm²}$

3. Filled volume = that slice's area × the tank length

   $12.566371\times 7$$=87.964594\text{\hspace{0.17em}cm³}$

4. Convert the filled volume to liters (1 cm³ = 0.001 L)

   $87.964594\times 0.001$$=0.087965\text{\hspace{0.17em}L}$

5. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{0.087965}{3.785411784}$$=0.023238\text{\hspace{0.17em}US gal}$

9. Liquid in the tank: 48,000 L

1. Total volume = length × width × height

   $6\times 4\times 4$$=96\text{\hspace{0.17em}m³}$

2. Filled volume = length × width × liquid depth

   $6\times 4\times 2$$=48\text{\hspace{0.17em}m³}$

3. Convert the filled volume to liters (1 m³ = 1,000 L)

   $48\times \mathrm{1,000}$$=\mathrm{48,000}\text{\hspace{0.17em}L}$

4. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{\mathrm{48,000}}{3.785411784}$$=\mathrm{12,680.258513}\text{\hspace{0.17em}US gal}$

10. Liquid in the tank: 0.05 L

1. Total volume = π × radius² × length

   $\pi \times 2^2\times 8$$=100.530965\text{\hspace{0.17em}cm³}$

2. Seen from the end, the liquid fills a slice of the circle (a circular segment). Its area, using radius r and depth h, is r² × arccos((r − h) ÷ r) − (r − h) × √(2rh − h²)

   $2^2\times \text{arccos}\left(\frac{2-2}{2}\right)-\left(2-2\right)\times \sqrt{2\times 2\times 2-2^2}$$=6.283185\text{\hspace{0.17em}cm²}$

3. Filled volume = that slice's area × the tank length

   $6.283185\times 8$$=50.265482\text{\hspace{0.17em}cm³}$

4. Convert the filled volume to liters (1 cm³ = 0.001 L)

   $50.265482\times 0.001$$=0.050265\text{\hspace{0.17em}L}$

5. Convert to US gallons (1 US gal = 3.785411784 L)

   $\frac{0.050265}{3.785411784}$$=0.013279\text{\hspace{0.17em}US gal}$