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\[ h(4) = h_0 - 16. \] - AIKO, infinite ways to autonomy.

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The side length of the square is $a$. Since the circle is inscribed, its diameter is equal to the side length of the square, so $2r = a$. Therefore, the radius $r = \frac{a}{2}$.

📌 The area of the circle is $\pi r^2 = \pi \left(\frac{a}{2}\right)^2 = \frac{\pi a^2}{4}$.

📌 The area of the square is $a^2$.

📌 The ratio of the area of the circle to the area of the square is given by:

📌 \frac{\frac{\pi a^2}{4}}{a^2} = \frac{\pi}{4}

📌 Thus, the final answer is \(\boxed{\frac{\pi}{4}}\).

📌 A cylinder has a height equal to its radius $r$. A cone with the same radius $r$ and height $r$ is placed inside the cylinder. Determine the ratio of the volume of the cone to the volume of the cylinder.

📌 The volume of the cylinder is given by \(V_{\text{cylinder}} = \pi r^2 h = \pi r^2 \cdot r = \pi r^3\).

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