Mathematics

Mathematics

Problem

56. Group Activity Tunnel Problem A rectangular tunnel is cut through a mountain to make a road. The upper vertices of the rectangle are on the circle `x2+y2=400x^{2}+y^{2}=400`, as illustrated in the figure. ![](https://storage.googleapis.com/diraq-contents/question-bank/question-images/453ded8a4b3f/2025_11_21_a7069325c5b13c7228ecg-6.jpg) (a) Show that the cross-sectional area of the end of the tunnel is `400sin⁡2θ400 \sin 2 \theta`. (b) Find the dimensions of the rectangular end of the tunnel that maximizes its cross-sectional area.

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