To calculate the surface area of a right circular cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r h + 2\pi r^2 \]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height (or length) of the cylinder.
- The first term \( 2\pi r h \) represents the lateral surface area (the side surface).
- The second term \( 2\pi r^2 \) represents the area of the two circular bases.
Given:
- \( r = 1.5 \) feet
- \( h = 20 \) feet
- Use \( \pi = 3.14 \)
Now, let's calculate each part.
Step 1: Calculate the lateral surface area
\[ \text{Lateral Surface Area} = 2\pi r h = 2 \times 3.14 \times 1.5 \times 20 \]
Calculating: \[ \text{Lateral Surface Area} = 2 \times 3.14 \times 1.5 \times 20 = 2 \times 3.14 \times 30 = 6.28 \times 30 = 188.4 , \text{square feet} \]
Step 2: Calculate the area of the two bases
\[ \text{Area of the Bases} = 2\pi r^2 = 2 \times 3.14 \times (1.5^2) \]
Calculating \( 1.5^2 \): \[ 1.5^2 = 2.25 \]
So, \[ \text{Area of the Bases} = 2 \times 3.14 \times 2.25 = 6.28 \times 2.25 = 14.175 , \text{square feet} \]
Step 3: Calculate the total surface area
Now, add the lateral surface area and the area of the bases: \[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of the Bases} \] \[ \text{Total Surface Area} = 188.4 + 14.175 = 202.575 , \text{square feet} \]
Final Answer
The surface area of the log is approximately \( 202.58 , \text{square feet} \).