Answer :
To find the approximate surface area of a single cylindrical column, we need to determine both the lateral surface area and the top and bottom surfaces. Here’s a step-by-step breakdown:
1. Given Values:
- Height (h) of the cylinder = 3 meters.
- Radius (r) of the cylinder = 0.6 meters.
2. Lateral Surface Area:
The formula for the lateral surface area of a cylinder is given by:
[tex]\[ A_{\text{lateral}} = 2 \pi r h \][/tex]
By substituting the given values:
[tex]\[ A_{\text{lateral}} = 2 \pi (0.6) (3) \approx 11.31 \text{ m}^2 \][/tex]
3. Top and Bottom Surface Area:
Each circle (top and bottom) has an area given by:
[tex]\[ A_{\text{circle}} = \pi r^2 \][/tex]
Since there are two circles, the total area for the top and bottom is:
[tex]\[ A_{\text{top\&bottom}} = 2 \pi r^2 = 2 \pi (0.6)^2 \approx 2.26 \text{ m}^2 \][/tex]
4. Total Surface Area:
The total surface area of the cylinder is the sum of the lateral surface area and the top and bottom surface areas:
[tex]\[ A_{\text{total}} = A_{\text{lateral}} + A_{\text{top\&bottom}} \approx 11.31 \text{ m}^2 + 2.26 \text{ m}^2 = 13.57 \text{ m}^2 \][/tex]
So, the approximate surface area of a single column is:
[tex]\[ \boxed{13.57 \text{ m}^2} \][/tex]
Therefore, the correct answer is:
A. [tex]$13.57 \text{ m}^2$[/tex]
1. Given Values:
- Height (h) of the cylinder = 3 meters.
- Radius (r) of the cylinder = 0.6 meters.
2. Lateral Surface Area:
The formula for the lateral surface area of a cylinder is given by:
[tex]\[ A_{\text{lateral}} = 2 \pi r h \][/tex]
By substituting the given values:
[tex]\[ A_{\text{lateral}} = 2 \pi (0.6) (3) \approx 11.31 \text{ m}^2 \][/tex]
3. Top and Bottom Surface Area:
Each circle (top and bottom) has an area given by:
[tex]\[ A_{\text{circle}} = \pi r^2 \][/tex]
Since there are two circles, the total area for the top and bottom is:
[tex]\[ A_{\text{top\&bottom}} = 2 \pi r^2 = 2 \pi (0.6)^2 \approx 2.26 \text{ m}^2 \][/tex]
4. Total Surface Area:
The total surface area of the cylinder is the sum of the lateral surface area and the top and bottom surface areas:
[tex]\[ A_{\text{total}} = A_{\text{lateral}} + A_{\text{top\&bottom}} \approx 11.31 \text{ m}^2 + 2.26 \text{ m}^2 = 13.57 \text{ m}^2 \][/tex]
So, the approximate surface area of a single column is:
[tex]\[ \boxed{13.57 \text{ m}^2} \][/tex]
Therefore, the correct answer is:
A. [tex]$13.57 \text{ m}^2$[/tex]
