Use the image to answer the question.

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

Answer 1

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.

Answer 2

wrong

Answer 3

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.