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) its radius (ii) its slant height.

Explanation

Radius of the cylindrical bucket, `R=18 cm`.
Height fo the cylindrical bucket, H = 32 cm.
Volume of sand in the bucket `=piR^(2)H=(pixx18xx18xx32)cm^(3)`.
Let theradius of the conical heap be r.
Height of the conical heap, h=24 cm.
`"Volume of the conical heap "=1/3pir^(2)h=(1/3pixxr^(2)xx24)cm^(3)`
`=(8pir^(2))cm^(3).`
Volume of the conical heap = volume of sand in the bucket
`rArr" "8pir^(2)=pixx18xx18xx32rArrr^(2)=(18xx18xx32)/8=1296`
`rArr" "r=sqrt(1296)=36 cm .`
`"Slant height, "l = sqrt(r^(2)+h^(2))`

`=sqrt((36)^(2)+(24)^(2))cm=sqrt(1296+576)cm`
`=sqrt(1872)cm = 43.26 cm.`
`~~43.3" cm (correct to one decimal place)"`.