Multiple choice

Three solid spheres of copper, whose radii are $3$ cm, $4$ cm and $5$ cm respestively are melted into a single solid sphere of radius R. The value of R is

  1. $12$ cm
  2. $8$ cm
  3. $4$ cm
  4. $6$ cm
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D Correct answer
Explanation

The volume of the new sphere is the sum of the volumes of the three smaller spheres: (4/3)pi*R^3 = (4/3)pi*(3^3 + 4^3 + 5^3). R^3 = 27 + 64 + 125 = 216. Therefore, R = cube root of 216, which is 6 cm.

AI explanation

The volumes must be equal, so using the sphere volume formula 4/3 * pi * R^3, we set 4/3 * pi * (3^3 + 4^3 + 5^3) equal to 4/3 * pi * R^3. This gives R^3 = 27 + 64 + 125, which means R^3 = 216. Taking the cube root, we find R = 6 cm.

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