A cylindrical bucket, 32 cm high and 18 cm of radius of the base, 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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Height of cylindrical bucket(h1)=32 cm
Radius of the base of the bucket (r1)=18 cm
∴Volume of the sand in the cylindrical bucket=πr12h1
Height of conical heap (h2)=24 cm
let the radius of the conical heap=r2
∴Volume of the sand in conical heap=31πr22h2
According to the question
The volume of the sand in the cylindrical bucket=Volume of the sand in the conical shape
πr12h1=31πr22h2
⇒π×(18)2×32=31π×r22×24
⇒r22=243×182×32
⇒r22=182×4
⇒r2=18×2=36cm
Slant height of heap=r
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Height of cylindrical bucket(h1)=32 cm
Radius of the base of the bucket (r1)=18 cm
∴Volume of the sand in the cylindrical bucket=πr12h1
Height of conical heap (h2)=24 cm
let the radius of the conical heap=r2
∴Volume of the sand in conical heap=31πr22h2
According to the question
The volume of the sand in the cylindrical bucket=Volume of the sand in the conical shape
πr12h1=31πr22h2
⇒π×(18)2×32=31π×r22×24
⇒r22=243×182×32
⇒r22=182×4
⇒r2=18×2=36cm
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