Question
what is the surface area of this cylinder use pi = 3.14 and round you're answer to the nearest hundredth the radius is radius = 1 /2 × diameter = 1/ 2 × 6 = 3 and the height is 9 cm
Answers
GPT-4o mini
To calculate the surface area of a cylinder, you can use the formula:
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
where:
- \( r \) is the radius,
- \( h \) is the height.
From your calculation:
- The radius \( r = 3 \) cm (based on your \( r = \frac{1}{2} \times 6 \)),
- The height \( h = 9 \) cm.
Now, substituting the values into the formula:
1. **Calculate the area of the two bases** (which is \( 2\pi r^2 \)):
\[
2\pi r^2 = 2 \times 3.14 \times (3)^2 = 2 \times 3.14 \times 9 = 56.52 \text{ cm}^2
\]
2. **Calculate the lateral surface area** (which is \( 2\pi rh \)):
\[
2\pi rh = 2 \times 3.14 \times 3 \times 9 = 2 \times 3.14 \times 27 = 169.56 \text{ cm}^2
\]
3. **Add both areas together** to find the total surface area:
\[
\text{Surface Area} = 56.52 + 169.56 = 226.08 \text{ cm}^2
\]
Thus, the surface area of the cylinder is approximately **226.08 cm²** (rounded to the nearest hundredth).
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
where:
- \( r \) is the radius,
- \( h \) is the height.
From your calculation:
- The radius \( r = 3 \) cm (based on your \( r = \frac{1}{2} \times 6 \)),
- The height \( h = 9 \) cm.
Now, substituting the values into the formula:
1. **Calculate the area of the two bases** (which is \( 2\pi r^2 \)):
\[
2\pi r^2 = 2 \times 3.14 \times (3)^2 = 2 \times 3.14 \times 9 = 56.52 \text{ cm}^2
\]
2. **Calculate the lateral surface area** (which is \( 2\pi rh \)):
\[
2\pi rh = 2 \times 3.14 \times 3 \times 9 = 2 \times 3.14 \times 27 = 169.56 \text{ cm}^2
\]
3. **Add both areas together** to find the total surface area:
\[
\text{Surface Area} = 56.52 + 169.56 = 226.08 \text{ cm}^2
\]
Thus, the surface area of the cylinder is approximately **226.08 cm²** (rounded to the nearest hundredth).