Question

Area is 3ft. Height is 2ft. We want to wrap this cylinder in gift wrapping paper. what is the total surface area rounded to the nearest hundredth?

Answer 1

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

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

where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately \( 3.14 \).

You mentioned that the area is 3 ft, but to calculate the total surface area of the cylinder, we need to clarify that the area mentioned isn't directly related to \( r \) or \( h \). Given that height \( h = 2 \) ft, we will first need to find the radius \( r \) using the provided area, which we will assume is the area of the base of the cylinder.

The area of the base of the cylinder (which is a circle) is given by the formula:

\[
\text{Area of base} = \pi r^2
\]

Since you mentioned the area is 3 ft², we set this equal to the area of the base:

\[
\pi r^2 = 3
\]

To find \( r \):

\[
r^2 = \frac{3}{\pi} \approx \frac{3}{3.14} \approx 0.955
\]
\[
r \approx \sqrt{0.955} \approx 0.977 \text{ ft}
\]

Now we can substitute \( r \) and \( h \) back into the total surface area formula:

1. Calculate \( 2\pi r^2 \):

\[
2\pi r^2 = 2 \pi (0.977)^2 \approx 2 \pi (0.955) \approx 2 \cdot 3.14 \cdot 0.955 \approx 6.0 \text{ ft}^2
\]

2. Calculate \( 2\pi rh \):

\[
2\pi rh = 2 \pi (0.977)(2) \approx 4 \pi (0.977) \approx 4 \cdot 3.14 \cdot 0.977 \approx 12.16 \text{ ft}^2
\]

3. Now sum those results to find the total surface area:

\[
\text{Total Surface Area} \approx 6.0 + 12.16 \approx 18.16 \text{ ft}^2
\]

Finally, we round this to the nearest hundredth:

\[
\text{Total Surface Area} \approx 18.16 \text{ ft}^2
\]

Thus, the total surface area of the cylinder, rounded to the nearest hundredth, is **18.16 ft²**.