Surface Area of Cylinders Quick Check

Question

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Question
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

6.5 meters
6.5 meters

13 meters
13 meters

42 meters

Answer 1

The correct answer is 6.5 meters.

Explanation: The surface area of a cylinder can be calculated using the formula: 2πr^2 + 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder.

In this case, we can see that the diameter of the circles is 12 meters, so the radius is 6 meters. The height of the rectangle is the height of the cylinder, so it is the unknown we need to find.

The surface area is given as 715.92 meters^2, so we can set up the equation:
2(3.14)(6)^2 + 2(3.14)(6)(h) = 715.92
75.36 + 37.68h = 715.92
37.68h = 640.56
h = 640.56 / 37.68
h ≈ 6.5 meters

Therefore, the height of the cylinder is approximately 6.5 meters.