Question

Question
Natalia is getting ready to cut a log up into smaller pieces. The log is in the shape of a right circular cylinder. The length of the log is 20 feet, and the radius is 1.5
feet. Solve for the surface area. Use 3.14
for π
.(1 point)
feet2

Answer 1

To find the surface area of a right circular 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 (or length) of the cylinder.

Given:
- Radius \( r = 1.5 \) feet
- Height \( h = 20 \) feet
- Using \( \pi \approx 3.14 \)

First, we can calculate the two components of the surface area:

1. **Area of the two circular bases:**
\[
\text{Area of bases} = 2\pi r^2 = 2 \times 3.14 \times (1.5)^2
\]
Calculating \( (1.5)^2 \):
\[
(1.5)^2 = 2.25
\]
Now substituting back:
\[
\text{Area of bases} = 2 \times 3.14 \times 2.25 = 3.14 \times 4.5 = 14.13 \text{ square feet}
\]

2. **Area of the side (lateral area):**
\[
\text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 1.5 \times 20
\]
Calculating:
\[
2 \times 3.14 \times 1.5 \times 20 = 3.14 \times 60 = 188.40 \text{ square feet}
\]

Now, we add both areas together to find the total surface area:
\[
\text{Total Surface Area} = \text{Area of bases} + \text{Lateral Area} = 14.13 + 188.40 = 202.53 \text{ square feet}
\]

Thus, the surface area of the log is:
\[
\boxed{202.53} \text{ square feet}
\]