Use the image to answer the question.
An illustration shows a rectangle of unknown height with a circle of radius 3 feet attached to its top left and a circle of radius 3 feet attached to its bottom right.
If the surface area of the net diagram of the right circular cylinder is 395.64 feet2 , find the height of the net diagram. Use 3.14 for π .
(1 point)
feet
wrong
To find the height of the net diagram, we first need to find the lateral surface area of the right circular cylinder.
The lateral surface area of a cylinder is given by the formula: 2πrh, where r is the radius and h is the height.
In this case, the radius is 3 feet and the total lateral surface area is 395.64 feet2.
We can set up the equation:
2(3.14)(3)h = 395.64
18.84h = 395.64
h = 395.64 / 18.84
h ≈ 21 feet
Therefore, the height of the net diagram is approximately 21 feet.
Apologies for the mistake in the previous calculation. Let's correct it.
The net diagram consists of two circles with radius 3 feet and a rectangle of unknown height h and width 6 feet. The lateral surface area of the right circular cylinder is the sum of the areas of the two circles and the area of the rectangle.
The lateral surface area of a cylinder is given by 2πrh, where r is the radius and h is the height.
For the two circles:
2π(3)(h) = 6πh
For the rectangle:
6h
The total lateral surface area is given as 395.64 feet2:
6πh + 6h = 395.64
6πh + 6h = 395.64
6πh + 6h = 395.64
6(h(π + 1)) = 395.64
h(π + 1) = 65.94
h = 65.94 / (π + 1)
h = 65.94 / (3.14 + 1)
h = 65.94 / 4.14
h ≈ 15.93 feet
Therefore, the correct height of the net diagram is approximately 15.93 feet.