Surface Area Unit Test

To find the height of the curved surface of the right circular cylinder, we need to calculate the lateral surface area of the cylinder which is the sum of the areas of the two circles and the rectangle.

Given that the surface area is 522.81 feet², we can calculate the lateral surface area:

Let the height of the rectangle be h feet.

Lateral Surface Area = 2πr * h, where r is the radius of the circle (diameter 9 feet) which is 4.5 feet.

Lateral Surface Area = 2 * 3.14 * 4.5 * h
Lateral Surface Area = 28.26h

Now, the total surface area is given as 522.81 feet², which is the sum of the lateral surface area and the areas of the two circles.

522.81 = 28.26h + πr² + πr²
522.81 = 28.26h + 3.14 * 4.5 * 4.5 + 3.14 * 4.5 * 4.5

Solve for h:
522.81 = 28.26h + 63.585 + 63.585
522.81 = 28.26h + 127.17
28.26h = 522.81 - 127.17
28.26h = 395.64
h = 395.64 / 28.26
h ≈ 14 feet

Therefore, the height of the curved surface of the right circular cylinder is approximately 14 feet.