Question
A cylinder has a diameter of 20 cm and height of 20 cm. Find the surface area. Use 3.14 for pi. SA = 2 pi r square 2 + 2 pi rh
Answers
GPT-4o mini
To find the surface area (SA) of the cylinder, we will use the formula:
\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- Diameter = 20 cm, so the radius \( r = \frac{20}{2} = 10 \) cm.
- Height \( h = 20 \) cm.
- Use \( \pi = 3.14 \).
Now plug in the values into the surface area formula:
1. Calculate \( 2\pi r^2 \):
\[
2\pi r^2 = 2 \times 3.14 \times (10)^2 = 2 \times 3.14 \times 100 = 628 \text{ cm}^2
\]
2. Calculate \( 2\pi rh \):
\[
2\pi rh = 2 \times 3.14 \times 10 \times 20 = 2 \times 3.14 \times 200 = 1256 \text{ cm}^2
\]
3. Now, sum both areas to find the total surface area:
\[
\text{SA} = 628 + 1256 = 1884 \text{ cm}^2
\]
Thus, the surface area of the cylinder is \( 1884 \text{ cm}^2 \).
\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- Diameter = 20 cm, so the radius \( r = \frac{20}{2} = 10 \) cm.
- Height \( h = 20 \) cm.
- Use \( \pi = 3.14 \).
Now plug in the values into the surface area formula:
1. Calculate \( 2\pi r^2 \):
\[
2\pi r^2 = 2 \times 3.14 \times (10)^2 = 2 \times 3.14 \times 100 = 628 \text{ cm}^2
\]
2. Calculate \( 2\pi rh \):
\[
2\pi rh = 2 \times 3.14 \times 10 \times 20 = 2 \times 3.14 \times 200 = 1256 \text{ cm}^2
\]
3. Now, sum both areas to find the total surface area:
\[
\text{SA} = 628 + 1256 = 1884 \text{ cm}^2
\]
Thus, the surface area of the cylinder is \( 1884 \text{ cm}^2 \).