Question
A cylinder has a height of 8 cm and a radius of 3 cm. What is the surface area? Use 3.14 for π. Label the answer with the correct unit. (12 points; 2 per ? mark)
Formula: SA =2r2 + 2rh
SA =2 ? ?2 + 2 ? ? ? → SA = ?
Formula: SA =2r2 + 2rh
SA =2 ? ?2 + 2 ? ? ? → SA = ?
Answers
GPT-4o mini
To find the surface area (SA) of the cylinder, we can use the given formula:
\[
SA = 2\pi r^2 + 2\pi rh
\]
Given:
- Height (h) = 8 cm
- Radius (r) = 3 cm
We will use \(\pi \approx 3.14\).
Let's start by substituting the values into the formula.
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (3^2)
= 2 \times 3.14 \times 9
= 2 \times 28.26
= 56.52 \, \text{cm}^2
\]
2. Calculate the area of the curved surface:
\[
2\pi rh = 2 \times 3.14 \times 3 \times 8
= 2 \times 3.14 \times 24
= 6.28 \times 24
= 150.72 \, \text{cm}^2
\]
3. Add the two areas to find the total surface area:
\[
SA = 56.52 + 150.72 = 207.24 \, \text{cm}^2
\]
Thus, the surface area of the cylinder is:
\[
\boxed{207.24 \, \text{cm}^2}
\]
\[
SA = 2\pi r^2 + 2\pi rh
\]
Given:
- Height (h) = 8 cm
- Radius (r) = 3 cm
We will use \(\pi \approx 3.14\).
Let's start by substituting the values into the formula.
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (3^2)
= 2 \times 3.14 \times 9
= 2 \times 28.26
= 56.52 \, \text{cm}^2
\]
2. Calculate the area of the curved surface:
\[
2\pi rh = 2 \times 3.14 \times 3 \times 8
= 2 \times 3.14 \times 24
= 6.28 \times 24
= 150.72 \, \text{cm}^2
\]
3. Add the two areas to find the total surface area:
\[
SA = 56.52 + 150.72 = 207.24 \, \text{cm}^2
\]
Thus, the surface area of the cylinder is:
\[
\boxed{207.24 \, \text{cm}^2}
\]