Multiple choice

Three copper spheres of radii 3 cm, 4 cm and 5 cm are melted to form a large sphere. What is its radius?

  1. 12 cm

  2. 10 cm

  3. 8 cm

  4. 6 cm
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D Correct answer
Explanation

Volume of large sphere = sum of volumes of small spheres. (4/3) * pi * R^3 = (4/3) * pi * (3^3 + 4^3 + 5^3). R^3 = 27 + 64 + 125 = 216. R = cube root of 216 = 6.

AI explanation

The total volume remains unchanged, so using the sphere volume formula, four thirds multiplied by pi multiplied by the sum of the cubes of the radii equals four thirds multiplied by pi multiplied by the cube of the new radius. The sum of the cubes is 27 plus 64 plus 125, giving 216. Taking the cube root of 216 results in a new radius of 6 cm.

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