Question
math conexus surface area of cylinders quick check
Answers
GPT-4o mini
To calculate the surface area of a cylinder, you need to know its radius (r) and height (h). The formula for the surface area (SA) of a cylinder is:
\[
SA = 2\pi r(h + r)
\]
This formula consists of two parts:
1. The lateral (or curved) surface area: \(2\pi rh\)
2. The area of the two circular bases: \(2\pi r^2\)
So, if you add those two parts together, you arrive at the total surface area formula provided above.
### Steps to Calculate the Surface Area of a Cylinder:
1. Identify the radius (r) and height (h) of the cylinder.
2. Use the formula:
\[
SA = 2\pi r(h + r)
\]
3. Plug in the values for r and h.
4. Calculate the surface area.
### Quick Example:
If a cylinder has a radius of 3 units and a height of 5 units, the surface area would be:
1. \( r = 3 \), \( h = 5 \)
2. Plugging into the formula:
\[
SA = 2\pi (3)(5) + 2\pi (3^2)
\]
Which simplifies to:
\[
SA = 30\pi + 18\pi = 48\pi
\]
3. Approximately \( 48 \times 3.14 \approx 150.72 \) square units.
Feel free to ask if you have a specific problem or example to work through!
\[
SA = 2\pi r(h + r)
\]
This formula consists of two parts:
1. The lateral (or curved) surface area: \(2\pi rh\)
2. The area of the two circular bases: \(2\pi r^2\)
So, if you add those two parts together, you arrive at the total surface area formula provided above.
### Steps to Calculate the Surface Area of a Cylinder:
1. Identify the radius (r) and height (h) of the cylinder.
2. Use the formula:
\[
SA = 2\pi r(h + r)
\]
3. Plug in the values for r and h.
4. Calculate the surface area.
### Quick Example:
If a cylinder has a radius of 3 units and a height of 5 units, the surface area would be:
1. \( r = 3 \), \( h = 5 \)
2. Plugging into the formula:
\[
SA = 2\pi (3)(5) + 2\pi (3^2)
\]
Which simplifies to:
\[
SA = 30\pi + 18\pi = 48\pi
\]
3. Approximately \( 48 \times 3.14 \approx 150.72 \) square units.
Feel free to ask if you have a specific problem or example to work through!