Given the surface area of the net diagram of the right circular cylinder is 715.92 square meters, we can see from the diagram that the net consists of three rectangles: two rectangles with length equal to the circumference of the base of the cylinder and height equal to the height of the cylinder, and one rectangle with length equal to the height of the cylinder and width equal to the circumference of the base of the cylinder.
The formula for the surface area of a cylinder is:
Surface Area = 2πr(r + h)
where r is the radius of the cylinder and h is the height of the cylinder.
We are given that the surface area is 715.92 square meters, and we know that π = 3.14. We also know that the circumference of the cylinder's base is equal to the width of the net diagram, which is 56 meters.
Plugging in the values:
715.92 = 2(3.14)(r)(r + h)
715.92 = 6.28r^2 + 6.28rh
The width of the net is 56 meters, which is equal to the circumference:
56 = 2(3.14)r
r = 8.91 meters
Now, plug r back in:
715.92 = 6.28(8.91)^2 + 6.28(8.91)h
715.92 = 500.43 + 56.044h
215.49 = 56.044h
h ≈ 3.843 meters
Therefore, the height of the right circular cylinder is approximately 3.843 meters. None of the given options match exactly, so the closest option is 6.5 meters.
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Question
Use the image to answer the question.
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
6.5 meters
6.5 meters
16 meters
16 meters
13 meters
1 answer
3 answers