Giant Soup Can
We will use the approximate dimensions of the bike to estimate the dimensions of the soup can:
Mathematical Work | Process, Emotional Reactions, and Reflections… |
Step 1: Use the bike’s width to estimate the tank’s width(L) | I used the approximate dimensions of the bike and visualized the tank’s width as 3 times the bike’s width. |
- Bike’s width: 142 cm. | I felt confident about using the approximate dimensions of the bike. |
- Tank’s width L = 142×3 = 426 cm | I appreciated how the photo helped in visual estimation. |
Step 2: Use the bike’s height to estimate the tank’s height (Diameter) | I moved on to calculate the height proportionally. I used the approximate dimensions of the bike and visualized the tank’s height as 2.5 times the bike’s height. |
- Bike’s height: 91 cm. | I felt confident about using the bike’s height since it was clearly stated. |
- The tank’s height is approximately D = 91 × 2.5 = 227.5 cm | I felt good about using a clear proportionality factor here. |
Step 3: Calculate the tank’s diameter | I calculated the diameter based on the previous details. |
- The tank’s diameter is approximately equal to its height: D = 227.5 cm | I made this connection since the tank is cylindrical, and its diameter is effectively its height. |
Step 4: Calculate tank volume (V) | I proceeded to calculate the volume using geometry. |
- Formula for cylinder volume: V = | I was ready to plug in the numbers and complete the calculation. |
- Radius of the tank: r = = = 113.75 cm | I confirmed the radius calculation. |
- V = = | This felt straightforward, though the numbers are large. |
- V ≈ 17,321,664.24 cm³. V = 17,321.66 Liters | I converted this to liters. |
Step 4: Determine if the tank holds enough water to fight a fire | I compared the result to typical firefighting requirements. |
- Water needed for a house fire: ≈ 12,000 L. https://www2.gov.bc.ca/assets/gov/environment/air-land-water /laws-rules/interim_guidance_fire_prevention-water_use | This value gave me a benchmark for the tank’s capacity. |
- V = 17,321.66 Liters > 12,000 Litres | The tank’s capacity is sufficient to put out a house fire. I was satisfied with this conclusion. |
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