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

Question

feet. Solve for the surface area. Use 3.14
for π

Answer 1

To calculate the surface area of a right circular cylinder, you can use the formula:

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

Where:

• $r$ is the radius of the base of the cylinder.
• $h$ is the height (or length) of the cylinder.
• The first term $2\pi rh$ 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

$$\text{Lateral Surface Area}=2\pi rh=2\times 3.14\times 1.5\times 20$$

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 $202.58,\text{square feet}$.