A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
For cylindrical bucket,
Radius, r = 18 cm
Height, h = 32 cm
As we know,
Volume of cylinder = πr2h
Where r is base radius and h is height of cylinder.
Volume of sand in bucket = π(18)2(32) cm3
Also, For conical heap
Let the radius be r and height, h = 24 cm is given,
As we know,
Where r is base radius and h is height of cone
As the volume of sand is constant
Volume of sand in bucket = Volume of conical heap
π (18)2(32) = 8πr2
(18)(18)(4) = r2
r = 18(2) = 36 cm
Also, we know
l2 = h2 + r2, where h , r and l are height radius respectively.
l2 = (24)2 + (36)2 = 576 + 1296 = 1876
l = 43.267 cm
So, radius and slant height of heap are 36 cm and 43.267 cm respectively.