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Home » OFicinas Hacks: Unlock Free Services Most People Overlook! - Abbey Badges

OFicinas Hacks: Unlock Free Services Most People Overlook! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A circle is inscribed in a square with a side length of 10 cm. What is the area of the circle?

📌 The diameter of the circle equals the square's side, so the radius is 5 cm. The area is \( \pi \times 5^2 = 25\pi \) square cm.

📌 #### 25\pi

📌 A train travels from City A to City B, a distance of 300 km, at a speed of 100 km/h. On the return trip, it travels at 75 km/h due to maintenance work. What is the average speed for the entire journey?

📌 Total distance = 600 km. Time to B = 3 hours, time to A = 4 hours. Total time = 7 hours. Average speed = \( \frac{600}{7} \approx 85.71 \) km/h.

📌 #### \(\frac{600}{7}\)

📌 A rectangular prism has dimensions 4 cm by 6 cm by 8 cm. What is the length of the longest diagonal inside the prism?

📌 Use the 3D Pythagorean theorem: \( \sqrt{4^2 + 6^2 + 8^2} = \sqrt{16 + 36 + 64} = \sqrt{116} = 2\sqrt{29} \) cm.

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