Question

A cylindrical bucket 32cm high and with base diameter 36cm is filled with wheat. This bucket is emptied on the ground and conical heap is formed. If the height of the conical heap is 24cm. Find the radius and Slant height of the heap.​

Answer 1

Answer:

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, then find the radius and slant height of the heap.

Solution:

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

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