what is the total surface area in meters of a cylinder that is 12m in diameter and 14m in height
circumference = 2 pi * 6
height = 14
so area of sides = 28 *6 * pi
then add the area of the top plus the bottom
pi (6)^2 + pi (6)^2
To find the total surface area of a cylinder, you need to sum the areas of the two circular bases and the lateral surface area.
1. Start by calculating the area of one circular base:
The formula for the area of a circle is A = πr^2, where r is the radius.
Given that the diameter of the cylinder is 12m, we can find the radius by dividing it by 2:
Radius (r) = Diameter / 2 = 12m / 2 = 6m
Now, calculate the area of one circular base:
Base Area = π(6m)^2 = 36π square meters (m^2)
2. Next, calculate the lateral surface area of the cylinder:
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height.
Lateral Surface Area = 2πrh = 2π(6m)(14m) = 168π square meters (m^2)
3. Finally, calculate the total surface area by adding the areas of the two circular bases and the lateral surface area:
Total Surface Area = Base Area + Base Area + Lateral Surface Area
= 36π + 36π + 168π
= 240π square meters (m^2)
Therefore, the total surface area of the cylinder is 240π square meters or approximately 753.98 square meters when rounded to two decimal places.