Question

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied out 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.

Answer 1

As we know if a solid object turn into another or if a thing which take a shape of one object turn into another object then there volume will be equal.
Take pie = ¶
volume of cylinder = volume of cone
¶×rsquare×h= 1/3¶r square h
18×18×32×3/24=r square
18×18×8×3/6= r square
18×18×4×3/3=r square
√18×18×2×2=r
18×2=r
r =36 cm
h= 24 cm
slant height = √36×36+24×24
slant height = √1872
slant height=
√2×2×2×2×13×3×3
slant height = 12√13 cm

Height (h1) of cylindrical bucket = 32 cm

Radius (r1) of circular end of bucket = 18 cm

Height (h2) of conical heap = 24 cm

Let the radius of the circular end of conical heap be r2.

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

r2 == 36 cm

Slant height =

Therefore, the radius and slant height of the conical heap are 36 cm andrespectively.