A cylinder container has a base radius of 6m and it's height is 17m.calculate it's total surface area with both end closed.
two circular baces: 2πr^2
curved lateral area (just a rectangle with length=base_circumference and the cylinder height): 2πrh
so now just plug in your numbers
To calculate the total surface area of a closed cylinder, we need to find the areas of both the top and bottom circles, as well as the lateral surface area.
1. Area of the top and bottom circles:
The formula for the area of a circle is A = π * r^2, where "r" is the radius.
Given that the base radius of the cylinder is 6m, we can calculate the area of each circle:
A = π * (6^2)
= π * 36
= 113.1m^2 (rounded to one decimal place)
2. Lateral surface area:
The formula for the lateral surface area of a cylinder is A = 2 * π * r * h, where "r" is the radius and "h" is the height.
Given that the height of the cylinder is 17m, we can calculate the lateral surface area:
A = 2 * π * 6 * 17
= 204πm^2 (exact value)
3. Total surface area:
The total surface area is the sum of the areas of the two circles and the lateral surface area.
A = 2 * (113.1) + (204π)
Using the value of π which is approximately 3.14159, we can calculate the total surface area:
A ≈ 2 * 113.1 + (204 * 3.14159)
≈ 226.2 + 641.84
≈ 868.04m^2 (rounded to two decimal places)
Therefore, the total surface area of the closed cylinder is approximately 868.04 square meters.