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The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.

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Very important question of mensuration including
very important concept of it.need solution!
Rd sharma class 10 maths exercise-16.3 mensuration.

we have to find the The height of a cone is 20 cm.
A small cone is cut off from the top by a plane
parallel to the base. If its volume be 1/125 of the
volume of the original cone.

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1 Answer

  1. Let the radius of the small cone be r cm

    Radius if the big cone = R cm

    Given, height of the big cone = 20 cm

    Let the height of section made = h cm

    Then, the height of small cone will be = (20 – h) cm

    Now,

    In △OAB and △OCD

    ∠AOB = ∠COD [common]

    ∠OAB = ∠OCD [each 90o]

    Then, OAB ~ △OCD [by AA similarity]

    So, by C.P.S.T we have

    OA/ OC = AB/ CD

    (20 – h)/ 20 = r/ R …… (i)

    Also given,

    Volume of small cone = 1/125 x volume of big cone

    1/3 π r2(20 – h) = 1/125 x 1/3 πR2 x 20

    r2/ R2 = 1/125 x 20/ (20 – h) [From (i)]

    (20 – h)2/ 202 = 1/125 x 20/20 – h

    (20 – h)3 = 203/ 125

    20 – h = 20/5

    20 – h = 4

    h = 20 – 4 = 16 cm

    Therefore, it’s found that the section was made at a height of 16 cm above the base.

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