Answer
**Cylindrical Tank:**
- **Capacity:** Approximately 1,232,000 litres
- **Volume to Fill:** 1,232,000 litres
- **Pumping Rate:** About 672,000 litres per hour
**Rectangular Tank:**
- **Height:** 1.125 meters
- **Initial Volume:** 1,620 litres
Solution
Sure, let's tackle the problems step-by-step. We'll address each question based on the information provided, making reasonable assumptions where necessary.
---
### **1. Cylindrical Tank Calculations**
**Given:**
- **Diameter of the tank (D)** = 28 meters
- **Height of the tank (h)** = 2 meters
**First, let's determine the radius (r) of the cylindrical tank:**
\[
r = \frac{D}{2} = \frac{28}{2} = 14 \text{ meters}
\]
#### **i) Capacity of the Tank in Litres**
**Formula for the volume of a cylinder:**
\[
\text{Volume} = \pi r^2 h
\]
**Calculations:**
\[
\text{Volume} = \pi \times (14)^2 \times 2 = \pi \times 196 \times 2 = 392\pi \text{ cubic meters}
\]
**Converting cubic meters to litres:**
\[
1 \text{ cubic meter} = 1000 \text{ litres}
\]
\[
\text{Capacity} = 392\pi \times 1000 \approx 392 \times 3.1416 \times 1000 \approx 1,232,000 \text{ litres}
\]
**Answer:**
The capacity of the tank is approximately **1,232,000 litres**.
#### **ii) Volume of Water Required to Fill the Tank in Litres**
Assuming the tank is initially empty:
\[
\text{Volume required} = \text{Total Capacity} = 1,232,000 \text{ litres}
\]
**Answer:**
The volume of water required to fill the tank is **1,232,000 litres**.
---
#### **iii) Rate at Which Water Was Pumped into the Tank**
**Given:**
- **Start Time:** 11:25 AM
- **End Time:** 1:15 PM
**Calculating the duration:**
\[
\text{From 11:25 AM to 1:15 PM} = 1 \text{ hour and } 50 \text{ minutes} = 1.833 \text{ hours}
\]
**Volume Pumped:**
Assuming the tank was filled from empty, the volume pumped is **1,232,000 litres**.
**Calculating the pumping rate:**
\[
\text{Rate} = \frac{\text{Volume}}{\text{Time}} = \frac{1,232,000 \text{ litres}}{1.833 \text{ hours}} \approx 672,000 \text{ litres/hour}
\]
**Answer:**
Water was pumped into the tank at a rate of approximately **672,000 litres per hour**.
---
### **2. Rectangular Tank Calculations**
**Given:**
- **Base Dimensions:** Length = 2.4 meters, Width = 2.4 meters (Assuming a square base since one dimension seems missing)
- **Capacity of the Tank:** 6,480 litres
#### **i) Finding the Height of the Tank in Meters**
**Converting litres to cubic meters:**
\[
6,480 \text{ litres} = 6.48 \text{ cubic meters}
\]
**Formula for the volume of a rectangular tank:**
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
**Given the base is assumed to be square:**
\[
\text{Area of Base} = 2.4 \times 2.4 = 5.76 \text{ square meters}
\]
**Calculating the height (h):**
\[
h = \frac{\text{Volume}}{\text{Area of Base}} = \frac{6.48}{5.76} = 1.125 \text{ meters}
\]
**Answer:**
The height of the tank is **1.125 meters**.
#### **ii) Initial Volume of Water When the Tank Was \( \frac{1}{4} \) Full**
**Given:**
- **Tank initially was \( \frac{1}{4} \) full**
**Calculating the initial volume:**
\[
\text{Initial Volume} = \frac{1}{4} \times \text{Total Capacity} = \frac{1}{4} \times 6,480 \text{ litres} = 1,620 \text{ litres}
\]
**Answer:**
Initially, the tank contained **1,620 litres** of water.
---
### **Summary of Answers**
1. **Cylindrical Tank:**
- **i)** Capacity ≈ **1,232,000 litres**
- **ii)** Volume to fill ≈ **1,232,000 litres**
- **iii)** Pumping rate ≈ **672,000 litres/hour**
2. **Rectangular Tank:**
- **i)** Height = **1.125 meters**
- **ii)** Initial volume = **1,620 litres**
---
**Note:**
For the rectangular tank, it was assumed that the base is square (2.4 m × 2.4 m) due to incomplete information. If the actual width is different, the height calculation will need to be adjusted accordingly.
Answered by UpStudy AI and reviewed by a Professional Tutor
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