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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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Very important question of mensuration including
very important concept of it.need solution!
Rd sharma class 10 maths exercise-16.1 mensuration.

we have to find the radius and slant height of the heap
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.

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1 Answer

  1. Given,

    Height of the cylindrical bucket = 32 cm

    Radius of the cylindrical bucket = 18 cm

    Height of conical heap = 24 cm

    We know that,

    Volume of cylinder = π × r2 × h

    And, volume of cone = 1/3 π × r2 × h

    Then, from the question

    Volume of the conical heap = Volume of the cylindrical bucket

    1/3 π × r2 × 24 = π × 182 × 32

    r2 = 182 x 4

    r = 18 x 2 = 36 cm

    Now,

    Slant height of the conical heap (l) is given by

    l = √(h2 + r2)

    l = √(242 + 362) = √1872

    l = 43.26 cm

    Therefore, the radius and slant height of the conical heap are 36 cm and 43.26 cm respectively.

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