An iron sheet of 221 cm × 218 cm × 1 cm dimension is molten. A sphere and a cube are formed from the molten material. If the side of cube and radius of the sphere formed are equal, then what is the radius of the sphere (in cm)?
Explanation:
Volume of iron sheet = 882 × 109 × 0.5 cm3
Let r be the radius of sphere which is equal to side of cube
Volume of sphere = 43πr3 = 43×227×r3 = 8821r3
Volume of cube = (side)3 = r3
Total volume of iron after reformation = 8821r3 + r3 = 10921r3
Volume of iron before reformation and after reformation should be same
⇒ 221 × 218 × 1 = 10921r3
⇒ r3 = 21 × 221 × 2
⇒ r3 = 21 × 441
⇒ r = 21
Hence, 21.
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