A cylindrical bucket 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is empted 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.
Answers
VOLUME OF THE CYLINDRICAL BUCKET
Given :
Height of the bucket = 32 cm
Radius = 18 cm
We know that :
Volume of a cylinder = π r² h
= π ( 18 )² × 32
= π × 324 × 32
= 10368 π
VOLUME OF CONICAL HEAP
Now , radius of the heap = ?
Let it be r
height of the heap = 24 cm
Volume = 1/3 π r² h
==> 1/3 × π × r² × 24
==> 8 π r²
Volume of both figures are same
So :
8 π r² = 10368 π
==> Cancelling π both sides :
==> 8 r² = 10368
==> r² = 10368/8
==> r² = 1296
==> r = 36 [ neglecting -ve ]
Hence radius = 36 cm
SLANT HEIGHT
Slant height = l² = r² + h² [ By Pythagoras Theorem ]
==> l² = ( 36 cm )² + ( 24 cm )²
==> l² = 1296 cm² + 576 cm²
==> l² = 1872 cm
==> l = √( 144 cm × 13 cm )
==> l = 12 cm ×√13
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ANSWERS
The radius is 36 cm
The slant height is 12√13 cm
Hope it helps :-)
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