Surface Area of Cylinders Quick Check

Question

2 of 52 of 5 Items

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

6.5 meters
6.5 meters

42 meters
42 meters

13 meters
13 meters

16 meters
16 meters
Skip to navigation

Answer 1

To find the height of the right circular cylinder, we need to find the lateral surface area of the cylinder and then use the formula: Lateral Surface Area = 2πrh

Given that the total surface area is 715.92 meters^2 and the circles have a diameter of 12 meters (radius = 6 meters), we can calculate the lateral surface area:

Total Surface Area = Lateral Surface Area + 2πr^2 (for the two circles)
715.92 = 2πrh + 2πr^2
715.92 = 2(3.14)(6)h + 2(3.14)(6)^2
715.92 = 37.68h + 226.08
489.84 = 37.68h
h ≈ 13 meters

Therefore, the height of the right circular cylinder is approximately 13 meters.

The correct answer is: 13 meters