Question
20 identical solid hemispheres of radius 3 cm are melted
to form a big solid hemisphere. What is the radius (in cm) of the biggest hemisphere formed, if 20% of the solid is wasted during the process?Solution
Given: Radius = 3 cm 20 hemispheres 20% wasted → 80% used Volume of 1 small hemisphere = (2/3)π(3³) = 18π Total volume = 20 × 18π = 360π Used volume = 360π × 0.8 = 288π Volume of big hemisphere = (2/3)πR³ = 288π ⇒ (2/3)R³ = 288 ⇒ R³ = 432 ⇒ R = ∛432 So, 432 = 6³ × 2 ⇒ ∛432 = 6∛2
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