https://file.aiquickdraw.com/mathbot/file/1724792807862q70pu5bp.jpg

The image shows a cylinder with a height of \( 35 \) cm and a diameter of \( 0.2 \) m. To calculate the surface area of the cylinder, we need to consider both the lateral surface area and the areas of the two circular bases.

### Step 1: Convert Units
The height is given in centimeters, and the diameter is given in meters. Let's convert the height to meters for consistency:

\[
35 \text{ cm} = 0.35 \text{ m}
\]

### Step 2: Identify Cylinder Parameters
- **Height (\( h \))**: \( 0.35 \) m
- **Diameter (\( d \))**: \( 0.2 \) m
- **Radius (\( r \))**: \( \frac{0.2}{2} = 0.1 \) m

### Step 3: Surface Area Formula
The total surface area (\( A \)) of a cylinder is calculated using the formula:

\[
A = 2\pi r h + 2\pi r^2
\]

Where:
- \( 2\pi r h \) is the lateral surface area.
- \( 2\pi r^2 \) is the area of the two circular bases.

### Step 4: Calculate the Lateral Surface Area
\[
2\pi r h = 2\pi (0.1)(0.35) = 0.07\pi \text{ m}^2
\]

### Step 5: Calculate the Area of the Two Circular Bases
\[
2\pi r^2 = 2\pi (0.1)^2 = 0.02\pi \text{ m}^2
\]

### Step 6: Calculate the Total Surface Area
\[
A = 0.07\pi + 0.02\pi = 0.09\pi \text{ m}^2
\]

Now, approximate the value of \( \pi \) (using \( \pi \approx 3.1416 \)):

\[
A \approx 0.09 \times 3.1416 \text{ m}^2 \approx 0.2827 \text{ m}^2
\]

### Final Answer
The total surface area of the cylinder is approximately **0.2827 square meters**.

Would you like any additional details or explanations?

Here are five related questions to deepen your understanding:
1. How would the surface area change if the height was doubled?
2. What is the surface area if the cylinder's radius was reduced by half?
3. How can you convert the surface area into square centimeters?
4. How would the volume of the cylinder be calculated?
5. What would the surface area be if the diameter was given in centimeters?

**Tip:** When calculating surface area, always ensure that all units are consistent before performing the calculations.

Learn how to calculate the surface area of a cylinder with a height of 35 cm and a diameter of 0.2 m. Includes step-by-step solution using the surface area formula for cylinders. Suitable for Grades 9-12 students and anyone interested in geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation