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 . (1 point) Responses 13 meters 13 meters 42 meters 42 meters 16 meters 16 meters 6.5 meters 6.5 meters
To find the height of the right circular cylinder, we first need to find the radius of the cylinder from the given surface area.
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr(r + h)
Given surface area = 715.92 m^2
Using π = 3.14
715.92 = 2(3.14)r(r + h)
357.96 = 3.14r^2 + 3.14rh
Dividing by 3.14:
113.943 = r^2 + rh
Now we also know that the total surface area of the cylinder must be 715.92 m^2.
The lateral surface area of a cylinder can be calculated as 2πrh.
Therefore, the lateral surface area = 2(3.14)r(h) = 6.28rh
So, 6.28rh must be equal to 715.92 - the area of the circular bases.
6.28rh = 715.92 - 113.943
6.28rh = 601.977
rh = 95.91
Now, we know that r = 3.14
Therefore, h = rh / 3.14 = 95.91 / 3.14 = 30.531
Therefore, the height of the right circular cylinder is approximately 30.53 meters.
The closest given option is 32 meters, so that would be the answer.