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Home » Time for second part: \(\frac20040 = 5\) hours. - AdVision eCommerce

Time for second part: \(\frac20040 = 5\) hours. - AdVision eCommerce

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Radius $ r = 3x $, height $ h = x $.

📌 Question: A neuropharmacologist is studying a circular electrode array of radius $ 2x $ cm, with a smaller hemispherical sensor of radius $ x $ cm embedded at its center. What is the ratio of the volume of the hemisphere to the volume of the full sphere with radius $ 2x $?

📌 Let the radius of the hemisphere be $ x $, and the full sphere have radius $ 2x $.

📌 Ratio of hemisphere volume to full sphere volume:

📌 Question: A synthetic biology lab is designing a circular petri dish with a radius of $ 4x $ cm. A regular hexagon is inscribed in the circle to arrange microplates evenly. What is the perimeter of the hexagon?

📌 Solution: In a regular hexagon inscribed in a circle, the side length equals the radius of the circle.

📌 Radius of the circle is $ 4x $, so each side of the hexagon is $ 4x $.

📌 Question: A climate adaptation model uses a right triangle to represent nutrient flow, where the legs measure $ 7x $ and $ 24x $ units. What is the sine of the angle opposite the shorter leg?

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