An illustration shows a horizontal rectangle of unknown height (in meters) with a circle of diameter 12 meters attached to its top left and a circle of diameter 12 meters attached to its bottom right.
If the surface area of the net diagram of the right circular cylinder is 715.92 meters2 , find the height. Use 3.14 for π .
To find the height of the cylinder, we first need to calculate the total surface area of the net diagram.
The net diagram consists of the lateral surface area of the cylinder and the areas of the two circles at the bases.
Given:
Diameter of the circles = 12 meters
Radius (r) of the circles = 12 / 2 = 6 meters
Area of one circle = πr^2
Area of one circle = 3.14 * 6^2 = 3.14 * 36 = 113.04 meters^2
Total area of both circles = 2 * 113.04 = 226.08 meters^2
Now, to find the lateral surface area of the cylinder:
Lateral surface area = 2πrh, where h is the height of the cylinder
Given total surface area = 226.08 + 2πrh = 715.92 meters^2
Therefore, 2πrh = 715.92 - 226.08 = 489.84 meters^2
Using the value of π as 3.14, we can now calculate the height:
2 * 3.14 * 6 * h = 489.84
37.68h = 489.84
h = 489.84 / 37.68
h ≈ 13 meters
Therefore, the height of the right circular cylinder is approximately 13 meters.