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
.
First, let's break down the net diagram into its components.
The rectangle has an unknown height and a width of 6 feet (the sum of the diameters of the two circles) since the circles have a radius of 3 feet.
The total surface area of the net diagram of the right circular cylinder is the sum of the areas of the rectangle and the two circles.
Rectangle area = height x width = height x 6
Circle area = πr^2 = 3.14 x 3^2
Total surface area = Rectangle area + 2(circle area)
395.64 = 6h + 2(3.14 x 3^2)
395.64 = 6h + 2(3.14 x 9)
395.64 = 6h + 56.52
339.12 = 6h
h = 339.12 / 6
h = 56.52 feet
Therefore, the height of the net diagram is 56.52 feet.
incorrect. whats the height of the square/rectangle?
To find the height of the rectangle in the net diagram, we need to consider the dimensions and positions of the circles attached to it.
Looking at the net diagram, we can see that the circles are attached in a way that their diameters form the width of the rectangle. Since the circles have a radius of 3 feet each, their diameters are 6 feet in total.
Therefore, the height of the rectangle is the distance between the centers of the two circles. This distance would be the diagonal of a rectangle with dimensions 6 feet by 6 feet (the diameters of the circles).
Using the Pythagorean theorem, we can find the height of the rectangle (h):
h^2 = 6^2 + 6^2
h^2 = 36 + 36
h^2 = 72
h ≈ √72
h ≈ 8.49 feet
Therefore, the height of the rectangle in the net diagram is approximately 8.49 feet.