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Home » Check using Pythagorean theorem: \( a^2 + b^2 = c^2 \) - Portal da AcÃºstica

Check using Pythagorean theorem: \( a^2 + b^2 = c^2 \) - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: Compute $ \cos 360^\circ $.

📌 Solution: The cosine of $ 360^\circ $ corresponds to the x-coordinate of the point on the unit circle at a full rotation from the positive x-axis. This point is $ (1, 0) $, so $ \cos 360^\circ = 1 $.

📌 Question: A cylinder has radius $ r $ and height $ 6r $. A cone has radius $ 2r $ and height $ 3r $. What is the ratio of the volume of the cylinder to the volume of the cone?

📌 Solution: The volume of the cylinder is $ V_{\text{cyl}} = \pi r^2 (6r) = 6\pi r^3 $. The volume of the cone is $ V_{\text{cone}} = \frac{1}{3} \pi (2r)^2 (3r) = \frac{1}{3} \pi (4r^2)(3r) = 4\pi r^3 $. The ratio is:

📌 \frac{V_{\text{cyl}}}{V_{\text{cone}}} = \frac{6\pi r^3}{4\pi r^3} = \frac{3}{2}.

📌 Question: A triangle has side lengths of $ 7 \, \text{cm} $, $ 10 \, \text{cm} $, and $ 13 \, \text{cm} $. What is the area of the triangle?

📌 Solution: Use Heron’s formula. The semi-perimeter is:

📌 s = \frac{7 + 10 + 13}{2} = 15 \, \text{cm}.

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