Questions: Find the surface area to the nearest whole number.

Solution Steps

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$^2$.

Final Answer