Question

Height 2 feet
Bass 6 ft

We want to wrap this cylinder in gift wrapping paper. What is the total surface area rounded to the nearest hundredth?

150f * t ^ 2

94.25f * t ^ 2

194.25f * t ^ 2

56.55f * t ^ 2

Answer 1

To find the total surface area of a cylinder, we can use the formula:

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

In this case, you have provided the height as 2 feet, but the base measurement of "6 ft" is unclear. It likely means the diameter of the base, hence:

- **Height (h)** = 2 feet
- **Diameter (d)** = 6 feet, thus the **Radius (r)** = \( \frac{d}{2} = \frac{6}{2} = 3 \) feet

Now we can calculate the surface area step-by-step.

1. **Calculate \( r^2 \)**:
\[
r^2 = 3^2 = 9 \text{ ft}^2
\]

2. **Calculate the area of the two bases**:
\[
2\pi r^2 = 2\pi(9) = 18\pi \text{ ft}^2
\]

3. **Calculate the lateral surface area (2πrh)**:
\[
2\pi rh = 2\pi(3)(2) = 12\pi \text{ ft}^2
\]

4. **Total Surface Area**:
\[
\text{Total Surface Area} = 2\pi r^2 + 2\pi rh = 18\pi + 12\pi = 30\pi \text{ ft}^2
\]

Now we can calculate this using the value of \(\pi \approx 3.14\):
\[
\text{Total Surface Area} \approx 30 \times 3.14 = 94.2 \text{ ft}^2
\]

Rounding to the nearest hundredth, the total surface area is approximately **94.25 ft²**.

Therefore, the correct answer is:

\(\boxed{94.25f \cdot t^2}\)