In a city, a tunnel will be built that crosses a mountain to facilitate the transit of automobiles and bicycles. Two projects were developed and the schemes with the front views of these projects are presented in the figure. Project 1 has two tunnels, one exclusive for bicycles and the other for automobiles. Project 2 has a single tunnel, with spaces reserved for exclusive transit of bicycles and automobiles. In both projects, the tunnels have the shape of a straight semicylinder of the same length, with two-way routes for both types of vehicles, separated by walls. The project to be approved will be the one that presents the smallest cross-sectional area, as it will imply a smaller volume of material removed from the mountain. Consider 3 as an approximation for $\pi$ and disregard the thicknesses of the walls. The project to be approved is (A) 1, as it presents a cross-sectional area measuring $67.5\,\mathrm{m}^2$. (B) 2, as it presents a cross-sectional area measuring $121.5\,\mathrm{m}^2$. (C) 1, as it presents a cross-sectional area measuring $135\,\mathrm{m}^2$. (D) 2, as it presents a cross-sectional area measuring $243\,\mathrm{m}^2$. (E) either one of the two, as they present cross-sectional areas with equal measurements.
In a city, a tunnel will be built that crosses a mountain to facilitate the transit of automobiles and bicycles. Two projects were developed and the schemes with the front views of these projects are presented in the figure.
Project 1 has two tunnels, one exclusive for bicycles and the other for automobiles. Project 2 has a single tunnel, with spaces reserved for exclusive transit of bicycles and automobiles. In both projects, the tunnels have the shape of a straight semicylinder of the same length, with two-way routes for both types of vehicles, separated by walls.
The project to be approved will be the one that presents the smallest cross-sectional area, as it will imply a smaller volume of material removed from the mountain.
Consider 3 as an approximation for $\pi$ and disregard the thicknesses of the walls.
The project to be approved is\\
(A) 1, as it presents a cross-sectional area measuring $67.5\,\mathrm{m}^2$.\\
(B) 2, as it presents a cross-sectional area measuring $121.5\,\mathrm{m}^2$.\\
(C) 1, as it presents a cross-sectional area measuring $135\,\mathrm{m}^2$.\\
(D) 2, as it presents a cross-sectional area measuring $243\,\mathrm{m}^2$.\\
(E) either one of the two, as they present cross-sectional areas with equal measurements.