A cylindrical bucket 32cm high and with base radius 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 conical heap is 24 cm find the radius and slant height of the heap
Answers
r=36
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Answer:
The radius and slant height of heap are 36 cm & 12√13 cm .
Step-by-step explanation:
Given :
Height of a cylindrical bucket , H = 32 cm
Radius of cylindrical bucket , R = 18 cm
Height of the conical heap of sand , h = 24 cm
Let the radius and slant height of the heap of sand be ‘r’ & ‘ l’.
Here, the sand filled in cylindrical bucket from a conical heap of sand on the ground. So volume of cylindrical bucket will be equal to the volume of conical heap.
Volume of cylindrical bucket = Volume of conical heap of sand
πR²H = 1/3 πr²h
R²H = 1/3 r²h
18² × 32 = ⅓ × r² × 24
18 × 18 × 32 = 8r²
r² = (18 × 18 × 32)/8
r² = 18 × 18 × 4
r² = 1296
r = √1296
r = 36 cm
Radius of the heap of sand = 36 cm
Slant height of the conical heap of sand, l = √(h² + r²
l = √24² + 36² = √(576 + 1296) = √1872
l = √144 × 13 = 12√13
l = 12√13 cm
slant height of the conical heap of sand, l = 12√13 cm
Hence the radius and slant height of heap are 36 cm & 12√13 cm .
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