First, we need to determine the lateral surface area of the cylinder.
The lateral surface area of a cylinder is given by the formula: 2πrh, where r is the radius of the base and h is the height of the cylinder.
In this case, the radius of the base is half of the diameter of the circle, so it is 4.5 feet.
Let's assume the height of the rectangle is x feet. Then the height of the cylinder would also be x feet.
So, the lateral surface area of the cylinder would be: 2 * 3.14 * 4.5 * x = 28.26x feet^2.
Since the total surface area of the net diagram is given as 522.81 feet^2, and the lateral surface area forms a rectangle in the net diagram, we can write the equation: 28.26x = 522.81.
Solving for x, we get: x = 522.81 / 28.26 ≈ 18.47 feet.
Therefore, the height of the curved surface of the cylinder is approximately 18.47 feet.
Surface Area Unit Test
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Question
Use the image to answer the question.
An illustration shows a horizontal rectangle of unknown height (in feet) with a circle of diameter 9 feet attached to its top left and a circle of diameter 9 feet attached to its bottom right.
The surface area of the net diagram of the right circular cylinder is 522.81 feet2. Find the height of the curved surface. Use 3.14 for π.
(1 point)
feet
1 answer