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

16 meters
16 meters

13 meters
13 meters

42 meters
42 meters

6.5 meters
6.5 meters
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1 answer

To find the height of the right circular cylinder based on the given surface area, we first need to understand the formula for the surface area of a cylinder.

The surface area \( A \) of a right circular cylinder is given by: \[ A = 2\pi r(h + r) \] where:

  • \( r \) is the radius of the base,
  • \( h \) is the height of the cylinder.

From the description, the diameter of the attached circles is 12 meters, so the radius \( r \) would be: \[ r = \frac{12}{2} = 6 \text{ meters} \]

Now, we can substitute the known values into the surface area equation: \[ 715.92 = 2 \pi (6)(h + 6) \]

Using \( \pi \approx 3.14 \): \[ 715.92 = 2 \times 3.14 \times 6 \times (h + 6) \] \[ 715.92 = 37.68 (h + 6) \]

Now, divide both sides by 37.68: \[ h + 6 = \frac{715.92}{37.68} \] \[ h + 6 \approx 19 \]

Now, subtract 6 from both sides: \[ h \approx 19 - 6 \] \[ h \approx 13 \]

Thus, the height of the cylinder is approximately 13 meters.

The correct response is: 13 meters.