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)
To find the surface area of a right circular cylinder, you need to calculate the lateral surface area and the area of the two circular bases.
The lateral surface area of a cylinder can be calculated using the formula: Lateral surface area = 2πrh, where r is the radius of the base and h is the height.
From the net diagram, we can see that the diameter of the circular base is 12 meters, so the radius is half of that: r = 12/2 = 6 meters.
Let's denote the height of the rectangle as h. The lateral surface area is 715.92 meters2, so we can set up the equation:
2π(6)(h) = 715.92
12πh = 715.92
h = 715.92 / (12π)
h ≈ 18.75 meters
Therefore, the height of the right circular cylinder is approximately 18.75 meters.
naw
I apologize for the error in my previous response. Let's try solving it again.
First, calculate the surface area of the two circles attached to the rectangle. Since the diameter of the circles is 12 meters, the radius is half of that, which is 6 meters.
The formula for the surface area of a circle is A = πr^2. So, the area of one circle would be:
A1 = π(6)^2
A1 = 36π meters2
Since there are two circles, the total area of the circles would be: 2(36π) = 72π meters2.
Now, subtract the area of the two circles from the total surface area of the net diagram:
715.92 meters2 - 72π meters2 = height * perimeter of the rectangle
715.92 - 72(3.14) = height * (2*12)
715.92 - 225.12 = 24h
490.8 = 24h
h = 490.8/24
h = 20.45 meters
Therefore, the height of the right circular cylinder is approximately 20.45 meters.
ur choises
13 meters
13 meters
16 meters
16 meters
6.5 meters
6.5 meters
42 meters
The correct answer is:
13 meters