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Question
A cylindrical bucket, 32 cm high and with radius of base 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.
Solution
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
`pixxr_1^2xxh_1=1/3pixxr_2^2xxh_2`
`pixx18^2xx32=1/3pixxr_2^2xx24`
`pixx18^2xx32= 1.3pixxr_2^2xx24`
`r_2^2= (3xx18^2xx32)/24 = 18^2 xx 4`
r2 = 18 x 2 = 36 cm
Slant height = `sqrt(36^2+24^2) = sqrt(12^2xx(3^2+2^2)) = 12sqrt13`
Therefore, the radius and slant height of the conical heap are 36 cm and
`12sqrt13` respectively
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