Hi!
I'm working on a math assignment and I was wondering if someone could check my math on this. PLZ!
Create a model of Tank B. Find the approximate capacity
Assuming that the overflow pipe is 100cm below the top of the tank, therefore the revised overflow height equals 0.9metres.
Depth Width Height Capacity (L)
Tank B - 1850mm OR 185cm 210cm -
Finding Approximate Capacity (without overflow)
Capacity = Volume converted into litres
Vtank = Abase x height
= Abase x 210
Abase = πr²
→In this case the width is equal to the diameter of the circle. Therefore the radius will equal 92.5cm
= π x 92.5²
≈ 8556.25
Vtank = 8556.25 x 210
= 1796812.5cm³
→ 1m³ = 1000000cm³
= 1796812.5 ÷ 1000000
= 1.7968125m³
Capacity = 1.7968125 m³ converted to litres
→1KL = 1m³
Capacity = 1.7968125KL
Finding Approximate Capacity (with overflow)
Assuming that the overflow pipe of the tank is 100mm or 10cm below the top
Depth Width Height Capacity (L)
Tank B - 1850mm OR 185cm 210cm -
Changed Overflow measurements - 185cm 110cm ?
Overflow Capacity = Volume converted into litres
Vtank = Abase x height
= Abase x 110
Abase = πr²
→In this case the width is equal to the diameter of the circle. Therefore the radius will equal 92.5cm
= π x 92.5²
≈ 8556.25
Vtank = 8556.25 x 110
= 941187.5cm³
→ 1m³ = 1000000cm³
= 941187.5 ÷ 1000000
= 0.9411875 m³
Overflow Capacity = 0.9411875 m³ converted to litres
→1KL = 1m³
Overflow Capacity = 0.9411875 KL
Answer
The normal capacity of the tank, when overflow is not being calculated, is 1.7968125KL. When overflow capacity is calculated, assuming that the overflow tank is 100cm from the top of the tank,
the capacity is equal to 0.9411875KL.
To check your math, let's break down the process of finding the approximate capacity of Tank B step by step:
1. Start by calculating the base area of the tank (Abase) using the formula Abase = πr², where r is the radius of the tank. In this case, the width is given as the diameter, so the radius will be half of that. Since the width is 185cm, the radius will be 92.5cm.
2. Calculate Abase = π(92.5)² ≈ 8556.25.
3. Next, calculate the volume of the tank (Vtank) by multiplying the base area (Abase) by the height of the tank. The height of the tank is given as 210cm.
4. Vtank = 8556.25 * 210 = 1796812.5 cm³.
5. Convert the tank volume to cubic meters (m³) by dividing by 1000000 (1m³ = 1000000cm³):
Vtank = 1796812.5 cm³ ÷ 1000000 = 1.7968125 m³.
6. Finally, convert the tank volume to liters by multiplying by 1000 (1m³ = 1000L):
Capacity = 1.7968125 m³ * 1000 = 1796.8125 L.
So the normal capacity of Tank B, without considering the overflow, is approximately 1796.8125 liters or 1.7968125KL (kiloliters).
To calculate the capacity considering the overflow, follow a similar process, but use the revised overflow measurements. In this case, the height of the overflow is given as 110cm. Repeat the steps above to find the overflow capacity:
1. Calculate the base area using the same formula: Abase = π(92.5)² ≈ 8556.25.
2. Calculate the volume of the overflow (Voverflow) by multiplying the base area (Abase) by the overflow height. The overflow height is given as 110cm.
3. Voverflow = 8556.25 * 110 = 941187.5 cm³.
4. Convert the overflow volume to cubic meters (m³) by dividing by 1000000:
Voverflow = 941187.5 cm³ ÷ 1000000 = 0.9411875 m³.
5. Finally, convert the overflow volume to liters by multiplying by 1000:
Overflow Capacity = 0.9411875 m³ * 1000 = 941.1875 L.
Therefore, the capacity of Tank B, taking the overflow into account, would be approximately 941.1875 liters or 0.9411875KL (kiloliters).
So, in conclusion, your math checks out. The normal capacity of the tank, without considering the overflow, is 1.7968125KL. When considering the overflow, assuming the overflow pipe is 100cm from the top of the tank, the capacity is approximately 0.9411875KL.