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 .
Answers
GPT 3.5
To solve for the surface area of the log, we need to calculate the lateral surface area and the surface area of the two circular faces.
Lateral Surface Area:
The lateral surface area of a right circular cylinder is given by the formula:
Lateral Surface Area = 2πrh
where r is the radius and h is the height (or length in this case) of the cylinder.
Given that the radius (r) is 1.5 feet and the length (h) is 20 feet:
Lateral Surface Area = 2 * 3.14 * 1.5 * 20
Lateral Surface Area = 188.4 square feet
Surface Area of the Circular Faces:
The surface area of a circle is given by the formula:
Surface Area of a Circle = πr^2
In this case, we have two circular faces, so the total surface area of the circular faces is:
Total Surface Area of Circular Faces = 2 * π * 1.5^2
Total Surface Area of Circular Faces = 2 * 3.14 * 2.25
Total Surface Area of Circular Faces = 14.13 square feet
Total Surface Area:
To find the total surface area of the log, we need to add the lateral surface area and the surface area of the circular faces together:
Total Surface Area = Lateral Surface Area + Total Surface Area of Circular Faces
Total Surface Area = 188.4 + 14.13
Total Surface Area = 202.53 square feet
Therefore, the surface area of the log is 202.53 square feet.
Lateral Surface Area:
The lateral surface area of a right circular cylinder is given by the formula:
Lateral Surface Area = 2πrh
where r is the radius and h is the height (or length in this case) of the cylinder.
Given that the radius (r) is 1.5 feet and the length (h) is 20 feet:
Lateral Surface Area = 2 * 3.14 * 1.5 * 20
Lateral Surface Area = 188.4 square feet
Surface Area of the Circular Faces:
The surface area of a circle is given by the formula:
Surface Area of a Circle = πr^2
In this case, we have two circular faces, so the total surface area of the circular faces is:
Total Surface Area of Circular Faces = 2 * π * 1.5^2
Total Surface Area of Circular Faces = 2 * 3.14 * 2.25
Total Surface Area of Circular Faces = 14.13 square feet
Total Surface Area:
To find the total surface area of the log, we need to add the lateral surface area and the surface area of the circular faces together:
Total Surface Area = Lateral Surface Area + Total Surface Area of Circular Faces
Total Surface Area = 188.4 + 14.13
Total Surface Area = 202.53 square feet
Therefore, the surface area of the log is 202.53 square feet.