Question
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)
To find the total surface area of the net diagram of the right circular cylinder, we need to find the surface area of the rectangle and the surface areas of the two circles.
The surface area of a rectangle is given by the formula: A = 2lw
The surface area of a circle is given by the formula: A = πr^2
Let the height of the rectangle be h. Then the length of the rectangle is also h.
Surface area of rectangle = 2(hh) = 2h^2
Surface area of circle 1 = π(3^2) = 9π
Surface area of circle 2 = π(3^2) = 9π
Total surface area = 2h^2 + 9π + 9π = 2h^2 + 18π
Given that the total surface area is 395.64 feet^2:
2h^2 + 18π = 395.64
2h^2 + 18(3.14) = 395.64
2h^2 + 56.52 = 395.64
2h^2 = 339.12
h^2 = 169.56
h = √169.56
h ≈ 13 feet
Therefore, the height of the net diagram is approximately 13 feet.