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.
Reviewed and approved by the UpStudy tutoring team
Explain
Simplify this solution
