A solid metal sphere of radius 32 cm is melted down and recast to make 64 identical small spheres. What will be the radius of each small sphere?
Answer (2)
V 1 = 3 4 π R 3 R = 32 c m V 1 = 3 4 π ⋅ 3 2 3 = 3 131072 π ( c m 3 ) V 2 = V 1 : 64 V 2 = 64 131072 π : 64 = 3 131072 π ⋅ 64 1 = 3 2048 π ( c m 3 ) r = ? V 2 = 3 4 π r 3
3 4 π r 3 = 3 2048 π / : π 3 4 r 3 = 3 2048 / ⋅ 4 3 r 3 = 512 r = 3 512 r = 8 ( c m ) ← an s w er
Each of the small spheres has a radius of 8 cm. This is calculated by first finding the volume of the original large sphere and then dividing that volume by the number of small spheres. Finally, we use the volume formula for spheres to find the radius of the small spheres.
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