https://file.aiquickdraw.com/mathbot/file/17266169249841tqu7k95.jpg

https://file.aiquickdraw.com/mathbot/file/1726616924986g1a5nk2d.jpg

Let's go through the steps in the provided math problem based on the images of the water storage tank.

### Information extracted from the images:
- **Height** of the water tank, \( h = 2.2 \, \text{m} \)
- **Diameter** of the tank, \( d = 1.8 \, \text{m} \)
  - This gives a **radius**, \( r = \frac{d}{2} = 0.9 \, \text{m} \)
- The problem asks for:
  - **5.1.2**: Find the radius.
  - **5.1.3**: Calculate the volume.
  - **5.1.4**: Calculate the volume of water at 90% capacity.
  - **5.1.5**: Calculate the surface area.

### Step-by-step solutions:

#### 5.1.2 Finding the Radius
From the image, the diameter \( d = 1.8 \, \text{m} \), so the radius \( r \) is:
\[
r = \frac{d}{2} = \frac{1.8}{2} = 0.9 \, \text{m}
\]
Thus, the radius of the tank is \( 0.9 \, \text{m} \).

#### 5.1.3 Calculate the Volume
The formula for the volume of a cylinder is:
\[
V = \pi r^2 h
\]
Using \( r = 0.9 \, \text{m} \), \( h = 2.2 \, \text{m} \), and \( \pi = 3.14 \):
\[
V = 3.14 \times (0.9)^2 \times 2.2
\]
Let me calculate this value for you.

#### 5.1.4 Volume at 90% Capacity
Once the volume from 5.1.3 is determined, 90% of the volume is calculated as:
\[
V_{90\%} = 0.9 \times V
\]
This will give us the volume of water in liters since \( 1 \, \text{m}^3 = 1000 \, \text{liters} \).

#### 5.1.5 Calculate the Total Surface Area
The formula for the surface area of a cylinder is:
\[
\text{Surface Area} = 2\pi r^2 + 2\pi r h
\]
Substitute \( r = 0.9 \, \text{m} \), \( h = 2.2 \, \text{m} \), and \( \pi = 3.14 \) into the equation to find the surface area.

Let me proceed with the calculations.Here are the results from the calculations:

### 5.1.3 Volume of the water storage tank:
\[
V = 5.60 \, \text{m}^3
\]

### 5.1.4 Volume of water at 90% capacity:
\[
V_{90\%} = 5036 \, \text{liters} \, (\text{rounded to the nearest liter})
\]

### 5.1.5 Total surface area of the water storage tank:
\[
\text{Surface Area} = 17.52 \, \text{m}^2
\]

Would you like further clarification or more details on any part of this? Here are some related questions:

1. How does the volume formula for a cylinder change if the height is doubled?
2. What would the surface area be if the radius was increased by 50%?
3. How do we calculate the lateral surface area of the tank alone?
4. How much water can be stored in the tank if it's filled to 80% of its capacity?
5. If the tank were made of a different material, would it affect the total surface area?

**Tip**: Remember that the volume of a cylinder increases with the square of the radius, so changes to the radius significantly impact capacity!

Given a cylindrical water storage tank with a height of 2.2 m and a diameter of 1.8 m, calculate the radius, volume, water volume at 90% capacity, and surface area.

This page explains how to find the radius, volume, and surface area of a cylindrical water storage tank with height 2.2 m and diameter 1.8 m. Learn how to calculate 90% of the tank's capacity in liters and understand the mathematical principles involved.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation