Question
A solid metal sphere of radius 6 cm is melted and recast
into solid hemispheres of radius 3 cm. How many such hemispheres are formed?Solution
Volume of sphere: V_sphere = (4/3)ΟRΒ³ = (4/3)Ο Γ 6Β³ = (4/3)Ο Γ 216 = 288Ο Volume of one hemisphere (radius 3 cm): V_hemi = (2/3)ΟrΒ³ = (2/3)Ο Γ 3Β³ = (2/3)Ο Γ 27 = 18Ο Number of hemispheres = 288Ο / 18Ο = 16.
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