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
.(1 point)
To solve for the surface area of the log, we need to find the lateral surface area and the top and bottom surface areas separately.
The lateral surface area of a cylinder can be calculated using the formula:
Lateral Surface Area = 2πrh
where r is the radius and h is the height (or in this case, the length).
Plugging in the values:
Lateral Surface Area = 2 * 3.14 * 1.5 * 20
Lateral Surface Area = 188.4 square feet
The top and bottom surface areas of a cylinder can be calculated using the formula:
Top/Bottom Surface Area = πr^2
Plugging in the values:
Top/Bottom Surface Area = 3.14 * 1.5^2
Top/Bottom Surface Area = 7.065 square feet
To find the total surface area, we add the lateral surface area to the sum of the top and bottom surface areas:
Total Surface Area = Lateral Surface Area + 2(Top/Bottom Surface Area)
Total Surface Area = 188.4 + 2(7.065)
Total Surface Area = 202.53 square feet
Therefore, the surface area of the log is 202.53 square feet.
A water tank is in the shape of a right circular cylinder. The diameter is 8 feet, and the height is 21.5 feet. Find the surface area of the water tank. Use 3.14 for π
.(1 point)
To find the surface area of the water tank, we need to calculate the lateral surface area and the top and bottom surface areas separately.
Given:
- Diameter = 8 feet, so radius (r) = 8/2 = 4 feet
- Height (h) = 21.5 feet
1. Lateral Surface Area:
Lateral Surface Area = 2πrh
Plugging in the values:
Lateral Surface Area = 2 * 3.14 * 4 * 21.5
Lateral Surface Area = 540.52 square feet
2. Top/Bottom Surface Area:
Top/Bottom Surface Area = 2πr^2
Plugging in the values:
Top/Bottom Surface Area = 2 * 3.14 * 4^2
Top/Bottom Surface Area = 100.48 square feet
3. Total Surface Area:
Total Surface Area = Lateral Surface Area + 2(Top/Bottom Surface Area)
Total Surface Area = 540.52 + 2(100.48)
Total Surface Area = 740.48 square feet
Therefore, the surface area of the water tank is 740.48 square feet.