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 .
Let's denote the height of the rectangle as h feet.
The curved surface area of a right circular cylinder is given by the formula:
Cylinder surface area = 2πrh
In this case, we have two circles attached to the rectangle forming the net diagram of the right circular cylinder, so the total surface area is:
Total Surface Area = 2πrh + πr^2 + πr^2
522.81 = 2(3.14)(9)h + 3.14(9)^2 + 3.14(9)^2
522.81 = 56.52h + 254.34
522.81 - 254.34 = 56.52h
268.47 = 56.52h
h = 268.47 / 56.52
h ≈ 4.75 feet
Therefore, the height of the curved surface of the right circular cylinder is approximately 4.75 feet.
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Let's denote the height of the rectangle as 'h' feet.
The curved surface area of a right circular cylinder is given by the formula:
Cylinder surface area = 2πrh
We are given that the surface area of the net diagram of the right circular cylinder is 522.81 square feet, which is the total surface area including the two circle areas and the curved surface area.
So, we have:
Total Surface Area = 2πrh + πr^2 + πr^2
522.81 = 2(3.14)(h)(9) + 3.14(9)^2 + 3.14(9)^2
522.81 = 56.52h + 254.34 + 254.34
522.81 = 56.52h + 508.68
Subtract 508.68 from both sides:
14.13 = 56.52h
Divide by 56.52:
h ≈ 0.25 feet
Therefore, the height of the curved surface of the right circular cylinder is approximately 0.25 feet.
Wrong
I apologize for the mistake. Let's reevaluate the solution.
Given:
Total Surface Area = 522.81 feet^2
Diameter of the circles = 9 feet
Let h be the height of the rectangle.
We know that the surface area of a right circular cylinder is the sum of the areas of the two circles and the lateral surface area.
Total Surface Area = 2πr^2 + 2πrh
Substitute the known values:
522.81 = 2(3.14)(4.5)^2 + 2(3.14)(4.5)h
522.81 = 169.29 + 28.26h
Rearrange the equation:
28.26h = 522.81 - 169.29
28.26h = 353.52
h = 353.52 / 28.26
h ≈ 12.5
Therefore, the height of the curved surface of the right circular cylinder is approximately 12.5 feet.