The surface area of a rectangular prism is given by \(2(lw + lh + wh)\), where \(l\), \(w\), and \(h\) are the length, width, and height respectively. In this case, \(l = 5\) ft, \(w = 3\) ft, and \(h = 3\) ft. Thus, the surface area is \(2(5 \cdot 3 + 5 \cdot 3 + 3 \cdot 3) = 2(15 + 15 + 9) = 2(39) = 78\) ft\(^2\).
The surface area of a cylinder is given by \(2\pi r^2 + 2\pi rh\), where \(r\) is the radius and \(h\) is the height. In this case, \(r = 3\) in and \(h = 6\) in. Thus, the surface area is \(2\pi(3^2) + 2\pi(3)(6) = 18\pi + 36\pi = 54\pi \approx 169.65\) in\(^2\). Rounding to the nearest whole number, we get \(170\) in\(^2\).
The surface area of a triangular prism is the sum of the areas of its faces. The triangular prism has two triangular bases and three rectangular faces. The area of each triangular base is \(\frac{1}{2}bh = \frac{1}{2}(10)(8) = 40\) m\(^2\). The rectangular faces have dimensions 9 m by 10 m, 9 m by 6 m, and 9 m by 8 m. Their areas are \(90\) m\(^2\), \(54\) m\(^2\), and \(72\) m\(^2\) respectively. The total surface area is \(2(40) + 90 + 54 + 72 = 80 + 90 + 54 + 72 = 296\) m\(^2\).
- \(\boxed{78}\) ft\(^2\)
- \(\boxed{170}\) in\(^2\)
- \(\boxed{296}\) m\(^2\)
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