Cylindrical bucket emptied into a cone
Geometry
Level
pending
A cylindrical bucket of 32 cm high and with radius of base 18 cm, is filled with sand completely. 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 slant height of the heap.
The answer is 43.266.
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1 solution
Volume of cylinder = pi *r^2 * h = pi * 18 * 18 *32
Volume of cone = 1/3 * pi * r1^2 * h1 = 1/3 *pi * r1^2 * 24
r1^2 = 3 *18 *18 *32/24 = 1296 so r = 36
Slant height = sqrt(36^2 + 24^2) = sqrt(12^2(9 + 4)) = 12*sqrt(13) = 43.266