Radius of cylinder = 18cm

Height= 24cm

Height of cone = 24cm!

volume of cylinder = πr2h

= π x 128 x 32

Volume of cone = 13πr2 x 24

The radius of cone can be calculated as follows:

r2=3×π×182×32π×24

Or, r2=182×22

Or, r = 36cm

So now the slant height of conical heap can be calculated as follows:

l = h2+r2−−−−−−√

l = h2+r2−−−−−−√= 242+362−−−−−−−−√

l = h2+r2−−−−−−√= 242+362−−−−−−−−√= 576+1296−−−−−−−−−√=1872−−−−√

Height of Bucket (h1) = 32cm

Base radius of Bucket (r1) = 18cm

Volume of sand in the bucket (V1) = π(r1)²h

Height of heap (h2) = 24cm

Radius of heap = r2

Volume of sand forming the heap(V2) = 1/3π(r2)²h2

Since, the sand is bucket is poured to form the heap, hence, the volume must be equal. That is, V1 = V2

π(r1)²h1 = 1/3π(r2)²h2

3*π(18)²32 = π(r2)²24

r2 = (18)²*4

r2 = 36 cm

Slant height of the heap formed is :

= √{(r1)²+(h2)²}

= √(36²+24²)

= √1872

= 12√13 cm

Thus, Radius of heap = 36cm Slant height of heap = 12√13 cm