Use the image to answer the question.
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 .
(1 point)
Responses
42 meters
42 meters
6.5 meters
6.5 meters
13 meters
13 meters
16 meters
16 meters
To find the height of the cylinder, we need to first find the radius of the circles at the top and bottom. Since the diameter is given as 12 meters, the radius would be 6 meters.
The surface area of a right circular cylinder is given by the formula:
Surface Area = 2πr^2 + 2πrh
We know that the total surface area is 715.92 meters^2, so we can substitute the values we have:
715.92 = 2 * 3.14 * 6^2 + 2 * 3.14 * 6 * h
715.92 = 226.08 + 37.68h
715.92 - 226.08 = 37.68h
489.84 = 37.68h
h = 12.96 meters
Therefore, the height of the cylinder is approximately 13 meters. Answer: 13 meters.