Height (h_{1}) of cylindrical bucket = 32 cm

Radius (r_{1}) of circular end of bucket = 18 cm

Height (h_{2}) of conical heap = 24 cm

Let the radius of the circular end of conical heap be r_{2}.

The volume of sand in the cylindrical bucket will be equal to the volume of sand in the conical heap.

Volume of sand in the cylindrical bucket = Volume of sand in conical heap

r_{2} = 18 x 2=36 cm

Slant height =

Therefore, the radius and slant height of the conical heap are 36 cm and 12√13 cm respectively