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Home » But area 504 may not yield integer. - AMAZONAWS

But area 504 may not yield integer. - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 An industrial designer develops a biodegradable packaging box in the shape of a rectangular prism with dimensions in the ratio 2:3:5. If the volume is 1080 cm³, what is the surface area in cm²?

📌 Let dimensions be 2x, 3x, 5x. Volume = 2x × 3x × 5x = 30x³ = 1080 → x³ = 36 → x = ∛36 ≈ 3.30

📌 So dimensions: 6.6, 9.9, 16.5 cm

📌 Surface area = 2(lw + lh + wh) = 2[(6.6×9.9) + (6.6×16.5) + (9.9×16.5)]

📌 = 2[65.34 + 108.9 + 163.35] = 2[337.59] = 675.18 cm²

📌 #### 675.18

📌 The James Webb Space Telescope images a galaxy cluster where the apparent angular separation between gravitational lenses is 0.8 arcseconds. If the cluster is 5 billion light-years away, and the lensing effect scales with mass and inverse distance, if a nearby cluster L tallies a separation of 1.6 arcseconds at equal distance, what is the ratio of the lensing mass of the distant cluster to the nearby one?

📌 Since apparent separation ∝ mass / distance, and distance is same (5 billion ly), then apparent separation ratio = mass ratio

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