7. 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.
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Answer:
Height of cylindrical bucket(h
1
)=32 cm
Radius of the base of the bucket (r
1
)=18 cm
∴Volume of the sand in the cylindrical bucket=πr
1
2
h
1
Height of conical heap (h
2
)=24 cm
let the radius of the conical heap=r
2
∴Volume of the sand in conical heap=
3
1
πr
2
2
h
2
According to the question
The volume of the sand in the cylindrical bucket=Volume of the sand in the conical shape
πr
1
2
h
1
=
3
1
πr
2
2
h
2
⇒π×(18)
2
×32=
3
1
π×r
2
2
×24
⇒r
2
2
=
24
3×18
2
×32
⇒r
2
2
=18
2
×4
⇒r
2
=18×2=36cm
Slant height of heap=
r
2
2
+h
2
2
⇒
36
2
+24
2
⇒
1296+576
⇒
1872
⇒
144×13
⇒12
13
cm.
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