Question

a sphere radius 6 cmis melted and recast in to a cone of height 6 cm . find the radius of the cone

Answer 1

volume of sphere=4/3×22/7×r^3
=4/3×22/7×6^3
volume of cone=1/3×22/7×r^2×h.
=1/3×22/7×r^2×6
since the sphere is melted and formed the cone, volumes of both will be equal.
so,
4/3×22/7×6^3=1/3×22/7×r^2×6
resolving the above equation
4×6^2=r^2
r^2=144
since radius cannot be -ve, r=12