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 13 meters 13 meters 16 meters 16 meters 6.5 meters
To find the height of the right circular cylinder, we need to examine the formula for the surface area of a cylinder:
Surface Area = 2πrh + 2πr^2
Given that the surface area is 715.92 meters^2 and that π=3.14, we have the equation:
715.92 = 2(3.14)r(h) + 2(3.14)r^2
Since we're looking for the height (h), let's isolate h in the equation:
715.92 = 6.28rh + 6.28r^2
715.92 - 6.28r^2 = 6.28rh
h = (715.92 - 6.28r^2) / 6.28r
Now, we need to find the radius of the right circular cylinder. Considering that the formula for the circumference of a cylinder is:
Circumference = 2πr
Given that the circumference is 42 (provided), we have:
42 = 2(3.14)r
42 = 6.28r
r = 6.67 meters (approximately)
Now, plug the radius back into the formula to find the height:
h = (715.92 - 6.28(6.67)^2) / 6.28(6.67)
h = (715.92 - 6.28(44.4889)) / 41.90
h = (715.92 - 280.05) / 41.90
h = 435.87 / 41.90
h ≈ 10.4 meters
Therefore, the height of the right circular cylinder is approximately 10.4 meters.
thats not a option the options are 42, 13, 16, 6.5
Let's correct the calculations to get one of the provided options.
Given:
Surface Area = 715.92 m^2
π = 3.14
Formula for the surface area of a cylinder:
Surface Area = 2πrh + 2πr^2
We are looking for the height (h), let's solve for h:
715.92 = 2(3.14)r(h) + 2(3.14)r^2
715.92 = 6.28rh + 6.28r^2
Given the circumference of the cylinder is 42 meters:
42 = 2(3.14)r
42 = 6.28r
r = 42 / 6.28
r ≈ 6.69 meters
Now substitute r back into the equation:
715.92 = 6.28(6.69)h + 6.28(6.69)^2
715.92 = 41.95h + 6.28(44.64)
715.92 = 41.95h + 281.87
41.95h = 715.92 - 281.87
41.95h = 434.05
h ≈ 434.05 / 41.95
h ≈ 10.36
Therefore, the height of the right circular cylinder is approximately 10.36 meters.
Since 10.36 is not one of the provided options, let's round it to the nearest whole number:
h ≈ 10 meters
Therefore, the closest option to the calculated height is 13 meters.