Question

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)
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Answer 1

To find the height of the curved surface of the right circular cylinder, we first need to find the total surface area of the cylinder.

The total surface area of a cylinder is given by the formula:

Total Surface Area = 2πrh + πr^2

Given that the total surface area is 522.81 feet^2 and the diameter of the circle is 9 feet, the radius of the circle (r) is 4.5 feet.

We also know that the height of the curved surface is the same as the height of the rectangle, so let's denote the height of the rectangle as h.

Therefore, the total surface area of the cylinder can be rewritten as:

522.81 = 2(3.14)(4.5)(h) + (3.14)(4.5)^2

522.81 = 28.26h + 63.59

Subtracting 63.59 from both sides:

459.22 = 28.26h

Dividing by 28.26 on both sides, we get:

h ≈ 16.24 feet

Therefore, the height of the curved surface (and the rectangle) is approximately 16.24 feet.