Three spheres of radii 6 cm, 8 cm and 10 cm are melted to form a sphere of radius
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11 cm
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13 cm
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24 cm
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none
Volume of new sphere = sum of volumes of three spheres. (4/3) * pi * R^3 = (4/3) * pi * (6^3 + 8^3 + 10^3). R^3 = 216 + 512 + 1000 = 1728. R = cube root of 1728 = 12 cm. Since 12 is not listed, 'none' is correct.
The sum of the volumes of the three original spheres equals the volume of the new sphere, using the sphere volume formula of 4 thirds times pi times the radius cubed. Adding the individual volumes gives the total as 4 thirds times pi multiplied by the sum of 6 cubed, 8 cubed, and 10 cubed, which equals 1728. Setting this equal to the new sphere's volume gives the new radius cubed as 1728, so the new radius is the cube root of 1728, resulting in exactly 12 cm. Since 12 cm is not provided among the choices, the correct answer is none.