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 .
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.