To find the surface area of a right circular cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius of the cylinder
- \( h \) is the height (or length) of the cylinder
Given:
- Radius, \( r = 1.5 \) feet
- Length (height), \( h = 20 \) feet
- Use \( \pi \approx 3.14 \)
Now we can calculate the surface area step by step.
- Calculate the area of the two circular bases:
\[ \text{Area of the bases} = 2\pi r^2 = 2 \times 3.14 \times (1.5)^2 \]
Calculating \( (1.5)^2 \): \[ (1.5)^2 = 2.25 \]
Now substitute back into the area formula: \[ = 2 \times 3.14 \times 2.25 = 2 \times 3.14 \times 2.25 = 14.13 \text{ square feet} \]
- Calculate the lateral surface area:
\[ \text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 1.5 \times 20 \]
Now calculate \( 2 \times 1.5 \times 20 \): \[ 2 \times 1.5 = 3 \] \[ 3 \times 20 = 60 \]
Now substitute back into the lateral area formula: \[ = 2 \times 3.14 \times 60 = 6.28 \times 60 = 376.8 \text{ square feet} \]
- Combine both areas to find the total surface area:
\[ \text{Total Surface Area} = \text{Area of the bases} + \text{Lateral Area} = 14.13 + 376.8 \] \[ = 390.93 \text{ square feet} \]
Thus, the surface area of the log is approximately \( \boxed{390.93} \) square feet.