A cylindrical bucket, 32 cm high and with radius of base 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 the conical heap is 24 cm, find the radius and slant height of the heap.
Answers
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 .
HOPE THIS ANSWER WILL HELP YOU…..
As we know if a solid object turn into another or if a thing which take a shape of one object turn into another object then there volume will be equal.
Take pie = ¶
volume of cylinder = volume of cone
¶×rsquare×h= 1/3¶r square h
18×18×32×3/24=r square
18×18×8×3/6= r square
18×18×4×3/3=r square
√18×18×2×2=r
18×2=r
r =36 cm
h= 24 cm
slant height = √36×36+24×24
slant height = √1872
slant height=
√2×2×2×2×13×3×3
slant height = 12√13 cm