Find the surface area for the given cylinder Use 3.14 for and round to the nearest whole number
6 ft 20 ft
1. 180 ft2
2. 720 ft2
3. 433
4. 135 ft2
720 ft2
explain why
The surface area of a cylinder formula is:
SA = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder.
In this question, the height of the cylinder is given as 20 ft, and we can assume that the radius is half of the diameter, which is given as 6 ft. Therefore, the radius is 3 ft.
Substituting these values in the formula:
SA = 2π(3)² + 2π(3)(20)
SA = 2π(9) + 2π(60)
SA = 18π + 120π
SA = 138π
Rounding to the nearest whole number using 3.14 for π:
SA = 138(3.14)
SA = 433 ft2 (rounded to the nearest whole number)
However, option 2, 720 ft2 is the correct answer, which suggests that there may have been an error in the question or the options given. Alternatively, there may have been some confusion between the surface area and lateral area of the cylinder.
To find the surface area of a cylinder, we need to calculate the sum of the areas of its curved surface (lateral surface area) and its two bases.
The formula for the lateral surface area of a cylinder is: LSA = 2πrh, where r is the radius of the base and h is the height of the cylinder.
Given:
Radius (r) = 6 ft
Height (h) = 20 ft
Using the formula for LSA, we have:
LSA = 2πrh
LSA = 2 * 3.14 * 6 * 20
LSA = 376.8 ft^2
The formula for the base area of a cylinder is: BA = πr^2
Using the formula for BA, we have:
BA = 3.14 * 6^2
BA = 3.14 * 36
BA = 113.04 ft^2
To find the total surface area, we sum the lateral surface area (LSA) and the base area (BA):
Total Surface Area = LSA + 2 * BA
Total Surface Area = 376.8 + 2 * 113.04
Total Surface Area = 376.8 + 226.08
Total Surface Area ≈ 602.88 ft²
Rounded to the nearest whole number, the surface area of the given cylinder is 603 ft².
Therefore, none of the given options is correct.