Question

A girl fills a cylindrical bucket 32 cm in height and
18 cm in radius with sand. She empties the bucket
on the ground and makes a conical heap of the sand.
If the height of the conical heap is 24 cm, find (i) the
radius and (ii) the slant height of the heap. Give your
answer correct to one place of decimal. (ICSE)​

Answer 1

Answer:

volume of the sand of cylindrical bucket used in making conical heap is same

volume of sand = volume of cylindrical bucket = πr^2h

now volume of cone = volume of cylinder

(1/3)πR^2H = πr^2h

R^2H = 3r^2h

R^2*24 = 3*18^2*32

R^2 = 3*324*32/24

R^2 = 1296

R = 36

slant height = √R^2 + H^2

= √ 36^2 + 24^2

= √1296 + 576

= 1872

= 12√13

= 43.3 cm