Multiple choice

Three solid spheres of gold whose radii are 1 cm, 6 cm and 8 cm respectively are melted into a single solid sphere. Find the radius of the sphere.

  1. 7 cm

  2. 8 cm

  3. 9 cm

  4. 10 cm
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C 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(1^3 + 6^3 + 8^3). This simplifies to R^3 = 1 + 216 + 512 = 729. Taking the cube root of 729 gives R = 9 cm.

AI explanation

When the three spheres are melted, the volume of the new solid sphere equals the sum of their volumes. The volume of a sphere is four thirds times pi times radius cubed, so the new radius cubed equals 1 cubed plus 6 cubed plus 8 cubed. Calculating this gives 1 plus 216 plus 512, which equals 729. The cube root of 729 is 9 cm.

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